Daily Papers

[This paper was initially published in PHME conference in 2016, selected for further publication in International Journal of Prognostics and Health Management.] This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM) for fault detection and prognostics of equipments based on sensors' data. It is a particular dynamic Bayesian network that allows to represent the dynamics of a system by means of a Hidden Markov Model (HMM) and an autoregressive (AR) process. The Markov chain assumes that the system is switching back and forth between internal states while the AR process ensures a temporal coherence on sensor measurements. A sound learning procedure of standard ARHMM based on maximum likelihood allows to iteratively estimate all parameters simultaneously. This paper suggests a modification of the learning procedure considering that one may have prior knowledge about the structure which becomes partially hidden. The integration of the prior is based on the Theory of Weighted Distributions which is compatible with the Expectation-Maximization algorithm in the sense that the convergence properties are still satisfied. We show how to apply this model to estimate the remaining useful life based on health indicators. The autoregressive parameters can indeed be used for prediction while the latent structure can be used to get information about the degradation level. The interest of the proposed method for prognostics and health assessment is demonstrated on CMAPSS datasets.

Autoregressive (AR) Large Language Models (LLMs) have demonstrated significant success across numerous tasks. However, the AR modeling paradigm presents certain limitations; for instance, contemporary autoregressive LLMs are trained to generate one token at a time, which can result in noticeable latency. Recent advances have indicated that search and repeated sampling can enhance performance in various applications, such as theorem proving, code generation, and alignment, by utilizing greater computational resources during inference. In this study, we demonstrate that diffusion language models are capable of generating at least 32 tokens simultaneously, while exceeding the performance of AR models in text quality and on the LAMBADA natural language understanding benchmark. This outcome is achieved through a novel distillation method for discrete diffusion models, which reduces the number of inference steps by a factor of 32-64. Practically, our models, even without caching, can generate tokens at a rate that is up to 8 times faster than AR models employing KV caching, and we anticipate further improvements with the inclusion of caching. Moreover, we demonstrate the efficacy of our approach for diffusion language models with up to 860M parameters.

Hidden Markov Models (HMMs) are foundational tools for modeling sequential data with latent Markovian structure, yet fitting them to real-world data remains computationally challenging. In this work, we show that pre-trained large language models (LLMs) can effectively model data generated by HMMs via in-context learning (ICL)x2013their ability to infer patterns from examples within a prompt. On a diverse set of synthetic HMMs, LLMs achieve predictive accuracy approaching the theoretical optimum. We uncover novel scaling trends influenced by HMM properties, and offer theoretical conjectures for these empirical observations. We also provide practical guidelines for scientists on using ICL as a diagnostic tool for complex data. On real-world animal decision-making tasks, ICL achieves competitive performance with models designed by human experts. To our knowledge, this is the first demonstration that ICL can learn and predict HMM-generated sequencesx2013an advance that deepens our understanding of in-context learning in LLMs and establishes its potential as a powerful tool for uncovering hidden structure in complex scientific data.

Large Language Models (LLMs) based on the pre-trained fine-tuning paradigm have become pivotal in solving natural language processing tasks, consistently achieving state-of-the-art performance. Nevertheless, the theoretical understanding of how model complexity influences fine-tuning performance remains challenging and has not been well explored yet. In this paper, we focus on autoregressive LLMs and propose to employ Hidden Markov Models (HMMs) to model them. Based on the HMM modeling, we investigate the relationship between model complexity and the generalization capability in downstream tasks. Specifically, we consider a popular tuning paradigm for downstream tasks, head tuning, where all pre-trained parameters are frozen and only individual heads are trained atop pre-trained LLMs. Our theoretical analysis reveals that the risk initially increases and then decreases with rising model complexity, showcasing a "double descent" phenomenon. In this case, the initial "descent" is degenerate, signifying that the "sweet spot" where bias and variance are balanced occurs when the model size is zero. Obtaining the presented in this study conclusion confronts several challenges, primarily revolving around effectively modeling autoregressive LLMs and downstream tasks, as well as conducting a comprehensive risk analysis for multivariate regression. Our research is substantiated by experiments conducted on data generated from HMMs, which provided empirical support and alignment with our theoretical insights.

Masked language model and autoregressive language model are two types of language models. While pretrained masked language models such as BERT overwhelm the line of natural language understanding (NLU) tasks, autoregressive language models such as GPT are especially capable in natural language generation (NLG). In this paper, we propose a probabilistic masking scheme for the masked language model, which we call probabilistically masked language model (PMLM). We implement a specific PMLM with a uniform prior distribution on the masking ratio named u-PMLM. We prove that u-PMLM is equivalent to an autoregressive permutated language model. One main advantage of the model is that it supports text generation in arbitrary order with surprisingly good quality, which could potentially enable new applications over traditional unidirectional generation. Besides, the pretrained u-PMLM also outperforms BERT on a set of downstream NLU tasks.

Autoregressive (AR) models have achieved unified and strong performance across both visual understanding and image generation tasks. However, removing undesired concepts from AR models while maintaining overall generation quality remains an open challenge. In this paper, we propose Erasure Autoregressive Model (EAR), a fine-tuning method for effective and utility-preserving concept erasure in AR models. Specifically, we introduce Windowed Gradient Accumulation (WGA) strategy to align patch-level decoding with erasure objectives, and Thresholded Loss Masking (TLM) strategy to protect content unrelated to the target concept during fine-tuning. Furthermore, we propose a novel benchmark, Erase Concept Generator and Visual Filter (ECGVF), aim at provide a more rigorous and comprehensive foundation for evaluating concept erasure in AR models. Specifically, we first employ structured templates across diverse large language models (LLMs) to pre-generate a large-scale corpus of target-replacement concept prompt pairs. Subsequently, we generate images from these prompts and subject them to rigorous filtering via a visual classifier to ensure concept fidelity and alignment. Extensive experimental results conducted on the ECGVF benchmark with the AR model Janus-Pro demonstrate that EAR achieves marked improvements in both erasure effectiveness and model utility preservation. Code is available at: https://github.com/immc-lab/ear/

The two dominant approaches to neural text generation are fully autoregressive models, using serial beam search decoding, and non-autoregressive models, using parallel decoding with no output dependencies. This work proposes an autoregressive model with sub-linear parallel time generation. Noting that conditional random fields with bounded context can be decoded in parallel, we propose an efficient cascaded decoding approach for generating high-quality output. To parameterize this cascade, we introduce a Markov transformer, a variant of the popular fully autoregressive model that allows us to simultaneously decode with specific autoregressive context cutoffs. This approach requires only a small modification from standard autoregressive training, while showing competitive accuracy/speed tradeoff compared to existing methods on five machine translation datasets.

Despite the success of autoregressive large language models in text generation, it remains a major challenge to generate text that satisfies complex constraints: sampling from the conditional distribution {Pr}(text | alpha) is intractable for even the simplest lexical constraints alpha. To overcome this challenge, we propose to use tractable probabilistic models (TPMs) to impose lexical constraints in autoregressive text generation models, which we refer to as GeLaTo (Generating Language with Tractable Constraints). To demonstrate the effectiveness of this framework, we use distilled hidden Markov models, where we can efficiently compute {Pr}(text | alpha), to guide autoregressive generation from GPT2. GeLaTo achieves state-of-the-art performance on challenging benchmarks for constrained text generation (e.g., CommonGen), beating various strong baselines by a large margin. Our work not only opens up new avenues for controlling large language models but also motivates the development of more expressive TPMs.

We introduce Autoregressive Diffusion Models (ARDMs), a model class encompassing and generalizing order-agnostic autoregressive models (Uria et al., 2014) and absorbing discrete diffusion (Austin et al., 2021), which we show are special cases of ARDMs under mild assumptions. ARDMs are simple to implement and easy to train. Unlike standard ARMs, they do not require causal masking of model representations, and can be trained using an efficient objective similar to modern probabilistic diffusion models that scales favourably to highly-dimensional data. At test time, ARDMs support parallel generation which can be adapted to fit any given generation budget. We find that ARDMs require significantly fewer steps than discrete diffusion models to attain the same performance. Finally, we apply ARDMs to lossless compression, and show that they are uniquely suited to this task. Contrary to existing approaches based on bits-back coding, ARDMs obtain compelling results not only on complete datasets, but also on compressing single data points. Moreover, this can be done using a modest number of network calls for (de)compression due to the model's adaptable parallel generation.

AutoRegressive (AR) models have made notable progress in image generation, with Masked AutoRegressive (MAR) models gaining attention for their efficient parallel decoding. However, MAR models have traditionally underperformed when compared to standard AR models. This study refines the MAR architecture to improve image generation quality. We begin by evaluating various image tokenizers to identify the most effective one. Subsequently, we introduce an improved Bidirectional LLaMA architecture by replacing causal attention with bidirectional attention and incorporating 2D RoPE, which together form our advanced model, MaskGIL. Scaled from 111M to 1.4B parameters, MaskGIL achieves a FID score of 3.71, matching state-of-the-art AR models in the ImageNet 256x256 benchmark, while requiring only 8 inference steps compared to the 256 steps of AR models. Furthermore, we develop a text-driven MaskGIL model with 775M parameters for generating images from text at various resolutions. Beyond image generation, MaskGIL extends to accelerate AR-based generation and enable real-time speech-to-image conversion. Our codes and models are available at https://github.com/synbol/MaskGIL.

Autoregressive models (ARMs) currently constitute the dominant paradigm for large language models (LLMs). Energy-based models (EBMs) represent another class of models, which have historically been less prevalent in LLM development, yet naturally characterize the optimal policy in post-training alignment. In this paper, we provide a unified view of these two model classes. Taking the chain rule of probability as a starting point, we establish an explicit bijection between ARMs and EBMs in function space, which we show to correspond to a special case of the soft Bellman equation in maximum entropy reinforcement learning. Building upon this bijection, we derive the equivalence between supervised learning of ARMs and EBMs. Furthermore, we analyze the distillation of EBMs into ARMs by providing theoretical error bounds. Our results provide insights into the ability of ARMs to plan ahead, despite being based on the next-token prediction paradigm.

Foundation models of time series have not been fully developed due to the limited availability of time series corpora and the underexploration of scalable pre-training. Based on the similar sequential formulation of time series and natural language, increasing research demonstrates the feasibility of leveraging large language models (LLM) for time series. Nevertheless, the inherent autoregressive property and decoder-only architecture of LLMs have not been fully considered, resulting in insufficient utilization of LLM abilities. To fully revitalize the general-purpose token transition and multi-step generation capability of large language models, we propose AutoTimes to repurpose LLMs as autoregressive time series forecasters, which projects time series into the embedding space of language tokens and autoregressively generates future predictions with arbitrary lengths. Compatible with any decoder-only LLMs, the consequent forecaster exhibits the flexibility of the lookback length and scalability with larger LLMs. Further, we formulate time series as prompts, extending the context for prediction beyond the lookback window, termed in-context forecasting. By introducing LLM-embedded textual timestamps, AutoTimes can utilize chronological information to align multivariate time series. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and over 5times training/inference speedup compared to advanced LLM-based forecasters. Code is available at this repository: https://github.com/thuml/AutoTimes.

Autoregressive (AR) models have long dominated the landscape of large language models, driving progress across a wide range of tasks. Recently, diffusion-based language models have emerged as a promising alternative, though their advantages over AR models remain underexplored. In this paper, we systematically study masked diffusion models in data-constrained settings-where training involves repeated passes over limited data-and find that they significantly outperform AR models when compute is abundant but data is scarce. Diffusion models make better use of repeated data, achieving lower validation loss and superior downstream performance. We interpret this advantage as implicit data augmentation: masked diffusion exposes the model to a diverse distribution of token orderings and prediction tasks, unlike AR's fixed left-to-right factorization. We find new scaling laws for diffusion models and derive a closed-form expression for the critical compute threshold at which diffusion begins to outperform AR. These results suggest that when data, not compute, is the bottleneck, diffusion models offer a compelling alternative to the standard AR paradigm. Our code is available at: https://diffusion-scaling.github.io.

Attention-based models such as Transformers and recurrent models like state space models (SSMs) have emerged as successful methods for autoregressive sequence modeling. Although both enable parallel training, none enable parallel generation due to their autoregressiveness. We propose the variational SSM (VSSM), a variational autoencoder (VAE) where both the encoder and decoder are SSMs. Since sampling the latent variables and decoding them with the SSM can be parallelized, both training and generation can be conducted in parallel. Moreover, the decoder recurrence allows generation to be resumed without reprocessing the whole sequence. Finally, we propose the autoregressive VSSM that can be conditioned on a partial realization of the sequence, as is common in language generation tasks. Interestingly, the autoregressive VSSM still enables parallel generation. We highlight on toy problems (MNIST, CIFAR) the empirical gains in speed-up and show that it competes with traditional models in terms of generation quality (Transformer, Mamba SSM).

Autoregressive (AR) models remain the standard for natural language generation but still suffer from high latency due to strictly sequential decoding. Recent diffusion-inspired approaches, such as LlaDA and Dream, mitigate this by generating in parallel, yet they suffer from two core limitations: information loss, as predictive distributions for non-finalized tokens are discarded at each step, and premature commitment, where local decisions are made without sufficient global coordination. We introduce Latent Refinement Decoding (LRD), a two-stage framework with Latent Refinement and a Predictive Feedback Loop. The first stage maintains masked positions as distributional mixtures of predicted tokens and the mask embedding, allowing the model to establish more globally consistent beliefs. The second stage progressively finalizes confident tokens while retaining uncertain ones for iterative feedback. KL-divergence dynamics provide a principled and reliable criterion for convergence and early stopping. Experiments across coding (HumanEval +6.3, MBPP +2.6) and reasoning (GSM8K +2.9, MATH500 +3.8) show that LRD improves accuracy while delivering speedups of up to 10.6x, making it a strong and versatile alternative for parallel sequence generation.

Context-aware STR methods typically use internal autoregressive (AR) language models (LM). Inherent limitations of AR models motivated two-stage methods which employ an external LM. The conditional independence of the external LM on the input image may cause it to erroneously rectify correct predictions, leading to significant inefficiencies. Our method, PARSeq, learns an ensemble of internal AR LMs with shared weights using Permutation Language Modeling. It unifies context-free non-AR and context-aware AR inference, and iterative refinement using bidirectional context. Using synthetic training data, PARSeq achieves state-of-the-art (SOTA) results in STR benchmarks (91.9% accuracy) and more challenging datasets. It establishes new SOTA results (96.0% accuracy) when trained on real data. PARSeq is optimal on accuracy vs parameter count, FLOPS, and latency because of its simple, unified structure and parallel token processing. Due to its extensive use of attention, it is robust on arbitrarily-oriented text which is common in real-world images. Code, pretrained weights, and data are available at: https://github.com/baudm/parseq.

Autoregressive modeling has been a huge success in the field of natural language processing (NLP). Recently, autoregressive models have emerged as a significant area of focus in computer vision, where they excel in producing high-quality visual content. Autoregressive models in NLP typically operate on subword tokens. However, the representation strategy in computer vision can vary in different levels, i.e., pixel-level, token-level, or scale-level, reflecting the diverse and hierarchical nature of visual data compared to the sequential structure of language. This survey comprehensively examines the literature on autoregressive models applied to vision. To improve readability for researchers from diverse research backgrounds, we start with preliminary sequence representation and modeling in vision. Next, we divide the fundamental frameworks of visual autoregressive models into three general sub-categories, including pixel-based, token-based, and scale-based models based on the strategy of representation. We then explore the interconnections between autoregressive models and other generative models. Furthermore, we present a multi-faceted categorization of autoregressive models in computer vision, including image generation, video generation, 3D generation, and multi-modal generation. We also elaborate on their applications in diverse domains, including emerging domains such as embodied AI and 3D medical AI, with about 250 related references. Finally, we highlight the current challenges to autoregressive models in vision with suggestions about potential research directions. We have also set up a Github repository to organize the papers included in this survey at: https://github.com/ChaofanTao/Autoregressive-Models-in-Vision-Survey.

Autoregressive (AR) large language models (LLMs) have achieved broad practical success, but sequential decoding remains a key bottleneck for low-latency deployment. Recent efficient-inference work has progressed along two axes: reducing the cost of each model invocation through efficient architectures, and reducing serial decoding steps through parallel generation. Hybrid attention backbones address the former, while diffusion language models (dLLMs) pursue the latter via iterative parallel denoising. Combining these advantages remains challenging: AR-to-dLLM conversion often fails to preserve seed-checkpoint capability, and hybrid-attention recurrent states and masking constraints make diffusion training and serving nontrivial. We present FLARE, a systematic conversion framework for hybrid-attention LLMs. Our analysis identifies transfer data quality as the primary determinant of capability preservation, outweighing loss formulation and attention-mask design. The resulting framework combines a token-equal AR-and-diffusion objective, hardware-aware kernels, and unified inference, enabling one checkpoint to support both AR-style verified decoding and diffusion-style parallel denoising. Starting from strong AR checkpoints with limited post-training data, FLARE is competitive with leading open-source dLLMs across model scales and delivers consistent throughput gains over open-source dLLM baselines in single-GPU concurrent serving. Our results further suggest that practical dLLMs are limited not only by decoding algorithms, but also by transfer data quality and the training inefficiency of current block-diffusion objectives, motivating joint design of data, objectives, architectures, and inference systems.

Autoregressive models are typically applied to sequences of discrete tokens, but recent research indicates that generating sequences of continuous embeddings in an autoregressive manner is also feasible. However, such Continuous Autoregressive Models (CAMs) can suffer from a decline in generation quality over extended sequences due to error accumulation during inference. We introduce a novel method to address this issue by injecting random noise into the input embeddings during training. This procedure makes the model robust against varying error levels at inference. We further reduce error accumulation through an inference procedure that introduces low-level noise. Experiments on musical audio generation show that CAM substantially outperforms existing autoregressive and non-autoregressive approaches while preserving audio quality over extended sequences. This work paves the way for generating continuous embeddings in a purely autoregressive setting, opening new possibilities for real-time and interactive generative applications.

As large language models (LMs) advance, there is an increasing need to control their outputs to align with human values (e.g., detoxification) or desired attributes (e.g., personalization, topic). However, autoregressive models focus on next-token predictions and struggle with global properties that require looking ahead. Existing solutions either tune or post-train LMs for each new attribute - expensive and inflexible - or approximate the Expected Attribute Probability (EAP) of future sequences by sampling or training, which is slow and unreliable for rare attributes. We introduce TRACE (Tractable Probabilistic Reasoning for Adaptable Controllable gEneration), a novel framework that efficiently computes EAP and adapts to new attributes through tractable probabilistic reasoning and lightweight control. TRACE distills a Hidden Markov Model (HMM) from an LM and pairs it with a small classifier to estimate attribute probabilities, enabling exact EAP computation over the HMM's predicted futures. This EAP is then used to reweigh the LM's next-token probabilities for globally compliant continuations. Empirically, TRACE achieves state-of-the-art results in detoxification with only 10% decoding overhead, adapts to 76 low-resource personalized LLMs within seconds, and seamlessly extends to composite attributes.

Historically, LLMs have been trained using either autoregressive (AR) or masked language modeling (MLM) objectives, with AR models gaining dominance in recent years. However, AR models are inherently incapable of masked infilling, which is the ability to predict masked tokens between past and future context. In contrast, MLM models suffer from intrinsic computational inefficiencies during both training and inference that hinder their scalability. This work introduces MARIA (Masked and Autoregressive Infilling Architecture), a novel approach that leverages the strengths of both paradigms to achieve state-of-the-art masked infilling performance. MARIA combines a pre-trained MLM and AR model by training a linear decoder that takes their concatenated hidden states as input. This minimal modification enables the AR model to perform infilling while retaining its inherent advantages in terms of faster inference with KV caching. Our results demonstrate that MARIA significantly outperforms existing methods, namely discrete diffusion models, on masked infilling tasks.

Autoregressive language models are constrained by their inherently sequential nature, generating one token at a time. This paradigm limits inference speed and parallelism, especially during later stages of generation when the direction and semantics of text are relatively certain. In this work, we propose a novel framework that leverages the inherent knowledge of vanilla autoregressive language models about future tokens, combining techniques to realize this potential and enable simultaneous prediction of multiple subsequent tokens. Our approach introduces several key innovations: (1) a masked-input formulation where multiple future tokens are jointly predicted from a common prefix; (2) a gated LoRA formulation that preserves the original LLM's functionality, while equipping it for multi-token prediction; (3) a lightweight, learnable sampler module that generates coherent sequences from the predicted future tokens; (4) a set of auxiliary training losses, including a consistency loss, to enhance the coherence and accuracy of jointly generated tokens; and (5) a speculative generation strategy that expands tokens quadratically in the future while maintaining high fidelity. Our method achieves significant speedups through supervised fine-tuning on pretrained models. For example, it generates code and math nearly 5x faster, and improves general chat and knowledge tasks by almost 2.5x. These gains come without any loss in quality.

In recent years, masked diffusion models (MDMs) have emerged as a promising alternative approach for generative modeling over discrete domains. Compared to autoregressive models (ARMs), MDMs trade off complexity at training time with flexibility at inference time. At training time, they must learn to solve an exponentially large number of infilling problems, but at inference time, they can decode tokens in essentially arbitrary order. In this work, we closely examine these two competing effects. On the training front, we theoretically and empirically demonstrate that MDMs indeed train on computationally intractable subproblems compared to their autoregressive counterparts. On the inference front, we show that a suitable strategy for adaptively choosing the token decoding order significantly enhances the capabilities of MDMs, allowing them to sidestep hard subproblems. On logic puzzles like Sudoku, we show that adaptive inference can boost solving accuracy in pretrained MDMs from <7% to approx 90%, even outperforming ARMs with 7times as many parameters and that were explicitly trained via teacher forcing to learn the right order of decoding.

Autoregressive models (ARMs) have become the workhorse for sequence generation tasks, since many problems can be modeled as next-token prediction. While there appears to be a natural ordering for text (i.e., left-to-right), for many data types, such as graphs, the canonical ordering is less obvious. To address this problem, we introduce a variant of ARM that generates high-dimensional data using a probabilistic ordering that is sequentially inferred from data. This model incorporates a trainable probability distribution, referred to as an order-policy, that dynamically decides the autoregressive order in a state-dependent manner. To train the model, we introduce a variational lower bound on the exact log-likelihood, which we optimize with stochastic gradient estimation. We demonstrate experimentally that our method can learn meaningful autoregressive orderings in image and graph generation. On the challenging domain of molecular graph generation, we achieve state-of-the-art results on the QM9 and ZINC250k benchmarks, evaluated using the Fr\'{e}chet ChemNet Distance (FCD).

Autoregressive (AR) models, long dominant in language generation, are increasingly applied to image synthesis but are often considered less competitive than Diffusion-based models. A primary limitation is the substantial number of image tokens required for AR models, which constrains both training and inference efficiency, as well as image resolution. To address this, we present Token-Shuffle, a novel yet simple method that reduces the number of image tokens in Transformer. Our key insight is the dimensional redundancy of visual vocabularies in Multimodal Large Language Models (MLLMs), where low-dimensional visual codes from visual encoder are directly mapped to high-dimensional language vocabularies. Leveraging this, we consider two key operations: token-shuffle, which merges spatially local tokens along channel dimension to decrease the input token number, and token-unshuffle, which untangles the inferred tokens after Transformer blocks to restore the spatial arrangement for output. Jointly training with textual prompts, our strategy requires no additional pretrained text-encoder and enables MLLMs to support extremely high-resolution image synthesis in a unified next-token prediction way while maintaining efficient training and inference. For the first time, we push the boundary of AR text-to-image generation to a resolution of 2048x2048 with gratifying generation performance. In GenAI-benchmark, our 2.7B model achieves 0.77 overall score on hard prompts, outperforming AR models LlamaGen by 0.18 and diffusion models LDM by 0.15. Exhaustive large-scale human evaluations also demonstrate our prominent image generation ability in terms of text-alignment, visual flaw, and visual appearance. We hope that Token-Shuffle can serve as a foundational design for efficient high-resolution image generation within MLLMs.

Autoregressive decoding is the only part of sequence-to-sequence models that prevents them from massive parallelization at inference time. Non-autoregressive models enable the decoder to generate all output symbols independently in parallel. We present a novel non-autoregressive architecture based on connectionist temporal classification and evaluate it on the task of neural machine translation. Unlike other non-autoregressive methods which operate in several steps, our model can be trained end-to-end. We conduct experiments on the WMT English-Romanian and English-German datasets. Our models achieve a significant speedup over the autoregressive models, keeping the translation quality comparable to other non-autoregressive models.

Autoregressive (AR) language models generate text one token at a time, even when consecutive tokens are highly predictable given earlier context. We introduce MARS (Mask AutoRegreSsion), a lightweight fine-tuning method that teaches an instruction-tuned AR model to predict multiple tokens per forward pass. MARS adds no architectural modifications, no extra parameters, and produces a single model that can still be called exactly like the original AR model with no performance degradation. Unlike speculative decoding, which maintains a separate draft model alongside the target, or multi-head approaches such as Medusa, which attach additional prediction heads, MARS requires only continued training on existing instruction data. When generating one token per forward pass, MARS matches or exceeds the AR baseline on six standard benchmarks. When allowed to accept multiple tokens per step, it maintains baseline-level accuracy while achieving 1.5-1.7x throughput. We further develop a block-level KV caching strategy for batch inference, achieving up to 1.71x wall-clock speedup over AR with KV cache on Qwen2.5-7B. Finally, MARS supports real-time speed adjustment via confidence thresholding: under high request load, the serving system can increase throughput on the fly without swapping models or restarting, providing a practical latency-quality knob for deployment.

Autoregressive models (ARMs), which predict subsequent tokens one-by-one ``from left to right,'' have achieved significant success across a wide range of sequence generation tasks. However, they struggle to accurately represent sequences that require satisfying sophisticated constraints or whose sequential dependencies are better addressed by out-of-order generation. Masked Diffusion Models (MDMs) address some of these limitations, but the process of unmasking multiple tokens simultaneously in MDMs can introduce incoherences, and MDMs cannot handle arbitrary infilling constraints when the number of tokens to be filled in is not known in advance. In this work, we introduce Insertion Language Models (ILMs), which learn to insert tokens at arbitrary positions in a sequence -- that is, they select jointly both the position and the vocabulary element to be inserted. By inserting tokens one at a time, ILMs can represent strong dependencies between tokens, and their ability to generate sequences in arbitrary order allows them to accurately model sequences where token dependencies do not follow a left-to-right sequential structure. To train ILMs, we propose a tailored network parameterization and use a simple denoising objective. Our empirical evaluation demonstrates that ILMs outperform both ARMs and MDMs on common planning tasks. Furthermore, we show that ILMs outperform MDMs and perform on par with ARMs in an unconditional text generation task while offering greater flexibility than MDMs in arbitrary-length text infilling.

In this work, we provide a systematic survey of Discrete Diffusion Language Models (dLLMs) and Discrete Diffusion Multimodal Language Models (dMLLMs). Unlike autoregressive (AR) models, dLLMs and dMLLMs adopt a multi-token, parallel decoding paradigm using full attention and a denoising-based generation strategy. This paradigm naturally enables parallel generation, fine-grained output controllability, and dynamic, response-aware perception. These capabilities are previously difficult to achieve with AR models. Recently, a growing number of industrial-scale proprietary d(M)LLMs, as well as a large number of open-source academic d(M)LLMs, have demonstrated performance comparable to their autoregressive counterparts, while achieving up to 10x acceleration in inference speed. The advancement of discrete diffusion LLMs and MLLMs has been largely driven by progress in two domains. The first is the development of autoregressive LLMs and MLLMs, which has accumulated vast amounts of data, benchmarks, and foundational infrastructure for training and inference. The second contributing domain is the evolution of the mathematical models underlying discrete diffusion. Together, these advancements have catalyzed a surge in dLLMs and dMLLMs research in early 2025. In this work, we present a comprehensive overview of the research in the dLLM and dMLLM domains. We trace the historical development of dLLMs and dMLLMs, formalize the underlying mathematical frameworks, and categorize representative models. We further analyze key techniques for training and inference, and summarize emerging applications across language, vision-language, and biological domains. We conclude by discussing future directions for research and deployment. Paper collection: https://github.com/LiQiiiii/DLLM-Survey

Although autoregressive models have dominated language modeling in recent years, there has been a growing interest in exploring alternative paradigms to the conventional next-token prediction framework. Diffusion-based language models have emerged as a compelling alternative due to their powerful parallel generation capabilities and inherent editability. However, these models are often constrained by fixed-length generation. A promising direction is to combine the strengths of both paradigms, segmenting sequences into blocks, modeling autoregressive dependencies across blocks while leveraging discrete diffusion to estimate the conditional distribution within each block given the preceding context. Nevertheless, their practical application is often hindered by two key limitations: rigid fixed-length outputs and a lack of flexible control mechanisms. In this work, we address the critical limitations of fixed granularity and weak controllability in current large diffusion language models. We propose CtrlDiff, a dynamic and controllable semi-autoregressive framework that adaptively determines the size of each generation block based on local semantics using reinforcement learning. Furthermore, we introduce a classifier-guided control mechanism tailored to discrete diffusion, which significantly reduces computational overhead while facilitating efficient post-hoc conditioning without retraining. Extensive experiments demonstrate that CtrlDiff sets a new standard among hybrid diffusion models, narrows the performance gap to state-of-the-art autoregressive approaches, and enables effective conditional text generation across diverse tasks.

Learning meaningful and general representations from unannotated speech that are applicable to a wide range of tasks remains challenging. In this paper we propose to use autoregressive predictive coding (APC), a recently proposed self-supervised objective, as a generative pre-training approach for learning meaningful, non-specific, and transferable speech representations. We pre-train APC on large-scale unlabeled data and conduct transfer learning experiments on three speech applications that require different information about speech characteristics to perform well: speech recognition, speech translation, and speaker identification. Extensive experiments show that APC not only outperforms surface features (e.g., log Mel spectrograms) and other popular representation learning methods on all three tasks, but is also effective at reducing downstream labeled data size and model parameters. We also investigate the use of Transformers for modeling APC and find it superior to RNNs.

As text generation has become a core capability of modern Large Language Models (LLMs), it underpins a wide range of downstream applications. However, most existing LLMs rely on autoregressive (AR) generation, producing one token at a time based on previously generated context-resulting in limited generation speed due to the inherently sequential nature of the process. To address this challenge, an increasing number of researchers have begun exploring parallel text generation-a broad class of techniques aimed at breaking the token-by-token generation bottleneck and improving inference efficiency. Despite growing interest, there remains a lack of comprehensive analysis on what specific techniques constitute parallel text generation and how they improve inference performance. To bridge this gap, we present a systematic survey of parallel text generation methods. We categorize existing approaches into AR-based and Non-AR-based paradigms, and provide a detailed examination of the core techniques within each category. Following this taxonomy, we assess their theoretical trade-offs in terms of speed, quality, and efficiency, and examine their potential for combination and comparison with alternative acceleration strategies. Finally, based on our findings, we highlight recent advancements, identify open challenges, and outline promising directions for future research in parallel text generation. We have also created a GitHub repository for indexing relevant papers and open resources available at https://github.com/zhanglingzhe0820/Awesome-Parallel-Text-Generation.

Autoregressive large language models (LLMs) have unified a vast range of language tasks, inspiring preliminary efforts in autoregressive video generation. Existing autoregressive video generators either diverge from standard LLM architectures, depend on bulky external text encoders, or incur prohibitive latency due to next-token decoding. In this paper, we introduce Lumos-1, an autoregressive video generator that retains the LLM architecture with minimal architectural modifications. To inject spatiotemporal correlations in LLMs, we identify the efficacy of incorporating 3D RoPE and diagnose its imbalanced frequency spectrum ranges. Therefore, we propose MM-RoPE, a RoPE scheme that preserves the original textual RoPE while providing comprehensive frequency spectra and scaled 3D positions for modeling multimodal spatiotemporal data. Moreover, Lumos-1 resorts to a token dependency strategy that obeys intra-frame bidirectionality and inter-frame temporal causality. Based on this dependency strategy, we identify the issue of frame-wise loss imbalance caused by spatial information redundancy and solve it by proposing Autoregressive Discrete Diffusion Forcing (AR-DF). AR-DF introduces temporal tube masking during training with a compatible inference-time masking policy to avoid quality degradation. By using memory-efficient training techniques, we pre-train Lumos-1 on only 48 GPUs, achieving performance comparable to EMU3 on GenEval, COSMOS-Video2World on VBench-I2V, and OpenSoraPlan on VBench-T2V. Code and models are available at https://github.com/alibaba-damo-academy/Lumos.

State-of-the-art language models are autoregressive and operate on subword units known as tokens. Specifically, one must encode the conditioning string into a list of tokens before passing to the language models for next-token prediction. We show that popular encoding schemes, such as maximum prefix encoding (MPE) and byte-pair-encoding (BPE), induce a sampling bias that cannot be mitigated with more training or data. To counter this universal problem, for each encoding scheme above, we propose a novel algorithm to obtain unbiased estimates from any language model trained on tokenized data. Our methods do not require finetuning the model, and the complexity, defined as the number of model runs, scales linearly with the sequence length in the case of MPE. As a result, we show that one can simulate token-free behavior from a tokenized language model. We empirically verify the correctness of our method through a Markov-chain setup, where it accurately recovers the transition probabilities, as opposed to the conventional method of directly prompting tokens into the language model.

Large language models (LLMs) have proven to be remarkably efficient, both across a wide range of natural language processing tasks and well beyond them. However, a comprehensive theoretical analysis of the origins of their impressive performance remains elusive. In this paper, we approach this challenging task by drawing an equivalence between generic autoregressive language models with vocabulary of size T and context window of size K and Markov chains defined on a finite state space of size O(T^K). We derive several surprising findings related to the existence of a stationary distribution of Markov chains that capture the inference power of LLMs, their speed of convergence to it, and the influence of the temperature on the latter. We then prove pre-training and in-context generalization bounds and show how the drawn equivalence allows us to enrich their interpretation. Finally, we illustrate our theoretical guarantees with experiments on several recent LLMs to highlight how they capture the behavior observed in practice.

Autoregressive models excel in modeling sequential dependencies by enforcing causal constraints, yet they struggle to capture complex bidirectional patterns due to their unidirectional nature. In contrast, mask-based models leverage bidirectional context, enabling richer dependency modeling. However, they often assume token independence during prediction, which undermines the modeling of sequential dependencies. Additionally, the corruption of sequences through masking or absorption can introduce unnatural distortions, complicating the learning process. To address these issues, we propose Bidirectional Autoregressive Diffusion (BAD), a novel approach that unifies the strengths of autoregressive and mask-based generative models. BAD utilizes a permutation-based corruption technique that preserves the natural sequence structure while enforcing causal dependencies through randomized ordering, enabling the effective capture of both sequential and bidirectional relationships. Comprehensive experiments show that BAD outperforms autoregressive and mask-based models in text-to-motion generation, suggesting a novel pre-training strategy for sequence modeling. The codebase for BAD is available on https://github.com/RohollahHS/BAD.

Diffusion language models enable any-order generation and bidirectional conditioning, offering appealing flexibility for tasks such as infilling, rewriting, and self-correction. However, their formulation-predicting one part of a sequence from another within a single-step dependency-limits modeling depth and often yields lower sample quality and stability than autoregressive (AR) models. To address this, we revisit autoregressive modeling as a foundation and reformulate diffusion-style training into a structured multi-group prediction process. We propose Any-order Any-subset Autoregressive modeling (A3), a generalized framework that extends the standard AR factorization to arbitrary token groups and generation orders. A3 preserves the probabilistic rigor and multi-layer dependency modeling of AR while inheriting diffusion models' flexibility for parallel and bidirectional generation. We implement A3 through a two-stream attention architecture and a progressive adaptation strategy that transitions pretrained AR models toward any-order prediction. Experiments on question answering, commonsense reasoning, and story infilling demonstrate that A3 outperforms diffusion-based models while maintaining flexible decoding. This work offers a unified approach for a flexible, efficient, and novel language modeling paradigm.

It is desirable but challenging to generate content-rich long videos in the scale of minutes. Autoregressive large language models (LLMs) have achieved great success in generating coherent and long sequences of tokens in the domain of natural language processing, while the exploration of autoregressive LLMs for video generation is limited to generating short videos of several seconds. In this work, we conduct a deep analysis of the challenges that prevent autoregressive LLM-based video generators from generating long videos. Based on the observations and analysis, we propose Loong, a new autoregressive LLM-based video generator that can generate minute-long videos. Specifically, we model the text tokens and video tokens as a unified sequence for autoregressive LLMs and train the model from scratch. We propose progressive short-to-long training with a loss re-weighting scheme to mitigate the loss imbalance problem for long video training. We further investigate inference strategies, including video token re-encoding and sampling strategies, to diminish error accumulation during inference. Our proposed Loong can be trained on 10-second videos and be extended to generate minute-level long videos conditioned on text prompts, as demonstrated by the results. More samples are available at: https://epiphqny.github.io/Loong-video.

Autoregressive (AR) large audio language models (LALMs) such as Qwen-2.5-Omni have achieved strong performance on audio understanding and interaction, but scaling them remains costly in data and computation, and strictly sequential decoding limits inference efficiency. Diffusion large language models (dLLMs) have recently been shown to make effective use of limited training data, and prior work on DIFFA indicates that replacing an AR backbone with a diffusion counterpart can substantially improve audio understanding under matched settings, albeit at a proof-of-concept scale without large-scale instruction tuning, preference alignment, or practical decoding schemes. We introduce DIFFA-2, a practical diffusion-based LALM for general audio understanding. DIFFA-2 upgrades the speech encoder, employs dual semantic and acoustic adapters, and is trained with a four-stage curriculum that combines semantic and acoustic alignment, large-scale supervised fine-tuning, and variance-reduced preference optimization, using only fully open-source corpora. Experiments on MMSU, MMAU, and MMAR show that DIFFA-2 consistently improves over DIFFA and is competitive to strong AR LALMs under practical training budgets, supporting diffusion-based modeling is a viable backbone for large-scale audio understanding. Our code is available at https://github.com/NKU-HLT/DIFFA.git.

In autoregressive language models, each token is sampled by conditioning on all the past tokens; the overall string has thus been sampled from the correct underlying joint distribution represented by the model. In contrast, masked diffusion language models generate text by unmasking tokens out of order and potentially in parallel. Generating an overall string sampled from the correct underlying joint distribution would (again) require exactly one token unmasking in every full-model forward pass. The more tokens unmasked in parallel, the further away the string is from the true joint; this can be seen in the resulting drop in accuracy (but, increase in speed). In this paper we devise a way to {\em approximately} sample multiple tokens from the joint distribution in a single full-model forward pass; we do so by developing a new lightweight single-layer ``sampler" on top of an existing large diffusion LM. One forward pass of the full model can now be followed by multiple forward passes of only this sampler layer, to yield multiple unmasked tokens. Our sampler is trained to mimic exact joint sampling from the (frozen) full model. We show the effectiveness of our approximate joint sampling for both pretrained-only (Dream-7B-Base) and instruction-tuned (Dream-7B-Instruct) models on language modeling and math \& coding tasks. When four tokens are unmasked for each full-model denoising step, our sampling algorithm achieves a MAUVE score of 0.87 (vs marginal baseline of 0.31) with respect to the true joint distribution.

Autoregressive (AR) models have reformulated image generation as next-token prediction, demonstrating remarkable potential and emerging as strong competitors to diffusion models. However, control-to-image generation, akin to ControlNet, remains largely unexplored within AR models. Although a natural approach, inspired by advancements in Large Language Models, is to tokenize control images into tokens and prefill them into the autoregressive model before decoding image tokens, it still falls short in generation quality compared to ControlNet and suffers from inefficiency. To this end, we introduce ControlAR, an efficient and effective framework for integrating spatial controls into autoregressive image generation models. Firstly, we explore control encoding for AR models and propose a lightweight control encoder to transform spatial inputs (e.g., canny edges or depth maps) into control tokens. Then ControlAR exploits the conditional decoding method to generate the next image token conditioned on the per-token fusion between control and image tokens, similar to positional encodings. Compared to prefilling tokens, using conditional decoding significantly strengthens the control capability of AR models but also maintains the model's efficiency. Furthermore, the proposed ControlAR surprisingly empowers AR models with arbitrary-resolution image generation via conditional decoding and specific controls. Extensive experiments can demonstrate the controllability of the proposed ControlAR for the autoregressive control-to-image generation across diverse inputs, including edges, depths, and segmentation masks. Furthermore, both quantitative and qualitative results indicate that ControlAR surpasses previous state-of-the-art controllable diffusion models, e.g., ControlNet++. Code, models, and demo will soon be available at https://github.com/hustvl/ControlAR.

The development of autoregressive modeling (AM) in computer vision lags behind natural language processing (NLP) in self-supervised pre-training. This is mainly caused by the challenge that images are not sequential signals and lack a natural order when applying autoregressive modeling. In this study, inspired by human beings' way of grasping an image, i.e., focusing on the main object first, we present a semantic-aware autoregressive image modeling (SemAIM) method to tackle this challenge. The key insight of SemAIM is to autoregressive model images from the semantic patches to the less semantic patches. To this end, we first calculate a semantic-aware permutation of patches according to their feature similarities and then perform the autoregression procedure based on the permutation. In addition, considering that the raw pixels of patches are low-level signals and are not ideal prediction targets for learning high-level semantic representation, we also explore utilizing the patch features as the prediction targets. Extensive experiments are conducted on a broad range of downstream tasks, including image classification, object detection, and instance/semantic segmentation, to evaluate the performance of SemAIM. The results demonstrate SemAIM achieves state-of-the-art performance compared with other self-supervised methods. Specifically, with ViT-B, SemAIM achieves 84.1% top-1 accuracy for fine-tuning on ImageNet, 51.3% AP and 45.4% AP for object detection and instance segmentation on COCO, which outperforms the vanilla MAE by 0.5%, 1.0%, and 0.5%, respectively.

Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.

Autoregressive (AR) generation is the standard decoding paradigm for Large Language Models (LLMs), but its token-by-token nature limits parallelism at inference time. Diffusion Language Models (DLLMs) offer parallel decoding by recovering multiple masked tokens per step; however, in practice they often fail to translate this parallelism into deployment speed gains over optimized AR engines (e.g., vLLM). A key reason is that many DLLMs rely on bidirectional attention, which breaks standard prefix KV caching and forces repeated contextualization, undermining efficiency. We propose WeDLM, a diffusion decoding framework built entirely on standard causal attention to make parallel generation prefix-cache friendly. The core idea is to let each masked position condition on all currently observed tokens while keeping a strict causal mask, achieved by Topological Reordering that moves observed tokens to the physical prefix while preserving their logical positions. Building on this property, we introduce a streaming decoding procedure that continuously commits confident tokens into a growing left-to-right prefix and maintains a fixed parallel workload, avoiding the stop-and-wait behavior common in block diffusion methods. Experiments show that WeDLM preserves the quality of strong AR backbones while delivering substantial speedups, approaching 3x on challenging reasoning benchmarks and up to 10x in low-entropy generation regimes; critically, our comparisons are against AR baselines served by vLLM under matched deployment settings, demonstrating that diffusion-style decoding can outperform an optimized AR engine in practice.

Autoregressive models have achieved impressive results over a wide range of domains in terms of generation quality and downstream task performance. In the continuous domain, a key factor behind this success is the usage of quantized latent spaces (e.g., obtained via VQ-VAE autoencoders), which allow for dimensionality reduction and faster inference times. However, using existing pre-trained models to perform new non-trivial tasks is difficult since it requires additional fine-tuning or extensive training to elicit prompting. This paper introduces LASS as a way to perform vector-quantized Latent Autoregressive Source Separation (i.e., de-mixing an input signal into its constituent sources) without requiring additional gradient-based optimization or modifications of existing models. Our separation method relies on the Bayesian formulation in which the autoregressive models are the priors, and a discrete (non-parametric) likelihood function is constructed by performing frequency counts over latent sums of addend tokens. We test our method on images and audio with several sampling strategies (e.g., ancestral, beam search) showing competitive results with existing approaches in terms of separation quality while offering at the same time significant speedups in terms of inference time and scalability to higher dimensional data.

Autoregressive language models (ARMs) are constrained by sequential, left-to-right generation, while masked diffusion models (MDMs) enable parallel decoding but suffer from high computational overhead due to the inability to reuse Key-Value (KV) cache and from incoherent generation arising from learning dependencies over an intractable space of token combinations. We introduce Zarya, a family of hybrid language models that jointly optimizes an autoregressive (AR) objective and a masked-diffusion objective within a single architecture. Zarya structures training data into variable-size slots and employs a curriculum that gradually increases slot granularity, enabling a smooth transition from fine-grained AR learning to coarse-grained diffusion learning. At inference, Zarya provides two distinct decoding paradigms through a unified interface: (i) MDM sampling with first-hitting denoising, and (ii) slotted speculative decoding that interleaves inter-slot diffusion-based selection with intra-slot autoregressive infilling, achieving full KV cache reuse. The training and inference regimes are fully decoupled, allowing a model trained with any configuration to be deployed in either mode. Extensive configurability --- including grouped noise patterns (Prefix Completion, Fill-In-the-Prefix, Fill-In-the-Middle), ordered sampling schedules, and noise-level permutation strategies --- enables flexible research exploration. We release Zarya models publicly in sizes 0.6B, 1.7B, and 4B, demonstrating performance on standard benchmarks while offering a principled integration of autoregressive and diffusion paradigms.

Autoregressive (AR) language models generate text one token at a time, which limits their inference speed. Diffusion-based language models offer a promising alternative, as they can decode multiple tokens in parallel. However, we identify a key bottleneck in current diffusion LMs: the long decoding-window problem, where tokens generated far from the input context often become irrelevant or repetitive. Previous solutions like semi-autoregressive address this issue by splitting windows into blocks (sacrificing bidirectionality), but we find that this also leads to time-interval expansion problem, sacrificing the speed. Therefore, semi-AR eliminates the main advantages of diffusion models. To overcome this, we propose Convolutional decoding (Conv), a normalization-based method that narrows the decoding window without hard segmentation, leading to better fluency and flexibility. Additionally, we introduce Rejecting Rule-based Fine-Tuning (R2FT), a post-hoc training scheme that better aligns tokens at positions far from context. Our methods achieve state-of-the-art results on open-ended generation benchmarks (e.g., AlpacaEval) among diffusion LM baselines, with significantly lower step size than previous works, demonstrating both speed and quality improvements.

Autoregressive (AR) language models have emerged as powerful solutions for zero-shot text-to-speech (TTS) synthesis, capable of generating natural speech from a few seconds of audio prompts. However, conventional AR-based TTS systems relying on discrete audio tokens face the challenge of lossy compression during tokenization, requiring longer discrete token sequences to capture the same information as continuous ones, which adds inference latency and complicates AR modeling. To address this challenge, this paper proposes the Continuous Latent Autoregressive model (CLEAR), a unified zero-shot TTS framework that directly models continuous audio representations. More specifically, CLEAR introduces an enhanced variational autoencoder with shortcut connections, which achieves a high compression ratio to map waveforms into compact continuous latents. A lightweight MLP-based rectified flow head that operates independently for each hidden state is presented to model the continuous latent probability distribution, and trained jointly with the AR model within a single-stage framework. Experiments show that the proposed zero-shot CLEAR TTS can synthesize high-quality speech with low latency. Compared to state-of-the-art (SOTA) TTS models, CLEAR delivers competitive performance in robustness, speaker similarity and naturalness, while offering a lower real-time factor (RTF). In particular, CLEAR achieves SOTA results on the LibriSpeech test-clean dataset, with a word error rate of 1.88\% and an RTF of 0.29. Moreover, CLEAR facilitates streaming speech synthesis with a first-frame delay of 96ms, while maintaining high-quality speech synthesis.

We introduce Dream 7B, the most powerful open diffusion large language model to date. Unlike autoregressive (AR) models that generate tokens sequentially, Dream 7B employs discrete diffusion modeling to refine sequences in parallel through iterative denoising. Our model consistently outperforms existing diffusion language models on general, mathematical, and coding tasks. Dream 7B demonstrates superior planning abilities and inference flexibility, including arbitrary-order generation, infilling capabilities, and tunable quality-speed trade-offs. These results are achieved through simple yet effective training techniques, including AR-based LLM initialization and context-adaptive token-level noise rescheduling. We release both Dream-Base and Dream-Instruct to facilitate further research in diffusion-based language modeling.

Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many tasks of interest -- including sequence continuation, infilling, and other forms of constrained generation -- involve sampling from intractable posterior distributions. We address this limitation by using amortized Bayesian inference to sample from these intractable posteriors. Such amortization is algorithmically achieved by fine-tuning LLMs via diversity-seeking reinforcement learning algorithms: generative flow networks (GFlowNets). We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training and reward-maximizing policy optimization. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem and demonstrate that our approach enables data-efficient adaptation of LLMs to tasks that require multi-step rationalization and tool use.

We propose a novel autoregressive modeling approach for speech synthesis, combining a variational autoencoder (VAE) with a multi-modal latent space and an autoregressive model that uses Gaussian Mixture Models (GMM) as the conditional probability distribution. Unlike previous methods that rely on residual vector quantization, our model leverages continuous speech representations from the VAE's latent space, greatly simplifying the training and inference pipelines. We also introduce a stochastic monotonic alignment mechanism to enforce strict monotonic alignments. Our approach significantly outperforms the state-of-the-art autoregressive model VALL-E in both subjective and objective evaluations, achieving these results with only 10.3\% of VALL-E's parameters. This demonstrates the potential of continuous speech language models as a more efficient alternative to existing quantization-based speech language models. Sample audio can be found at https://tinyurl.com/gmm-lm-tts.

Parameter-shared pre-trained language models (PLMs) have emerged as a successful approach in resource-constrained environments, enabling substantial reductions in model storage and memory costs without significant performance compromise. However, it is important to note that parameter sharing does not alleviate computational burdens associated with inference, thus impeding its practicality in situations characterized by limited stringent latency requirements or computational resources. Building upon neural ordinary differential equations (ODEs), we introduce a straightforward technique to enhance the inference efficiency of parameter-shared PLMs. Additionally, we propose a simple pre-training technique that leads to fully or partially shared models capable of achieving even greater inference acceleration. The experimental results demonstrate the effectiveness of our methods on both autoregressive and autoencoding PLMs, providing novel insights into more efficient utilization of parameter-shared models in resource-constrained settings.

Pretrained language models have achieved state-of-the-art performance when adapted to a downstream NLP task. However, theoretical analysis of these models is scarce and challenging since the pretraining and downstream tasks can be very different. We propose an analysis framework that links the pretraining and downstream tasks with an underlying latent variable generative model of text -- the downstream classifier must recover a function of the posterior distribution over the latent variables. We analyze head tuning (learning a classifier on top of the frozen pretrained model) and prompt tuning in this setting. The generative model in our analysis is either a Hidden Markov Model (HMM) or an HMM augmented with a latent memory component, motivated by long-term dependencies in natural language. We show that 1) under certain non-degeneracy conditions on the HMM, simple classification heads can solve the downstream task, 2) prompt tuning obtains downstream guarantees with weaker non-degeneracy conditions, and 3) our recovery guarantees for the memory-augmented HMM are stronger than for the vanilla HMM because task-relevant information is easier to recover from the long-term memory. Experiments on synthetically generated data from HMMs back our theoretical findings.

Autoregressive models (ARMs) are hindered by slow sequential inference. While masked diffusion models (MDMs) offer a parallel alternative, they suffer from critical drawbacks: high computational overhead from precluding Key-Value (KV) caching, and incoherent generation arising from learning dependencies over an intractable space of token combinations. To address these limitations, we introduce ReFusion, a novel masked diffusion model that achieves superior performance and efficiency by elevating parallel decoding from the token level to a higher slot level, where each slot is a fixed-length, contiguous sub-sequence. This is achieved through an iterative ``plan-and-infill'' decoding process: a diffusion-based planning step first identifies a set of weakly dependent slots, and an autoregressive infilling step then decodes these selected slots in parallel. The slot-based design simultaneously unlocks full KV cache reuse with a unified causal framework and reduces the learning complexity from the token combination space to a manageable slot-level permutation space. Extensive experiments on seven diverse benchmarks show that ReFusion not only overwhelmingly surpasses prior MDMs with 34% performance gains and an over 18times speedup on average, but also bridges the performance gap to strong ARMs while maintaining a 2.33times average speedup.

In many domains, autoregressive models can attain high likelihood on the task of predicting the next observation. However, this maximum-likelihood (MLE) objective does not necessarily match a downstream use-case of autoregressively generating high-quality sequences. The MLE objective weights sequences proportionally to their frequency under the data distribution, with no guidance for the model's behaviour out of distribution (OOD): leading to compounding error during autoregressive generation. In order to address this compounding error problem, we formulate sequence generation as an imitation learning (IL) problem. This allows us to minimize a variety of divergences between the distribution of sequences generated by an autoregressive model and sequences from a dataset, including divergences with weight on OOD generated sequences. The IL framework also allows us to incorporate backtracking by introducing a backspace action into the generation process. This further mitigates the compounding error problem by allowing the model to revert a sampled token if it takes the sequence OOD. Our resulting method, SequenceMatch, can be implemented without adversarial training or major architectural changes. We identify the SequenceMatch-chi^2 divergence as a more suitable training objective for autoregressive models which are used for generation. We show that empirically, SequenceMatch training leads to improvements over MLE on text generation with language models.

Autoregressive (AR) models, common in sequence generation, are limited in many biological tasks such as de novo peptide sequencing and protein modeling by their unidirectional nature, failing to capture crucial global bidirectional token dependencies. Non-Autoregressive (NAR) models offer holistic, bidirectional representations but face challenges with generative coherence and scalability. To transcend this, we propose a hybrid framework enhancing AR generation by dynamically integrating rich contextual information from non-autoregressive mechanisms. Our approach couples a shared input encoder with two decoders: a non-autoregressive one learning latent bidirectional biological features, and an AR decoder synthesizing the biological sequence by leveraging these bidirectional features. A novel cross-decoder attention module enables the AR decoder to iteratively query and integrate these bidirectional features, enriching its predictions. This synergy is cultivated via a tailored training strategy with importance annealing for balanced objectives and cross-decoder gradient blocking for stable, focused learning. Evaluations on a demanding nine-species benchmark of de novo peptide sequencing show that our model substantially surpasses AR and NAR baselines. It uniquely harmonizes AR stability with NAR contextual awareness, delivering robust, superior performance on diverse downstream data. This research advances biological sequence modeling techniques and contributes a novel architectural paradigm for augmenting AR models with enhanced bidirectional understanding for complex sequence generation. Code is available at https://github.com/BEAM-Labs/denovo.

Autoregressive (AR) modeling, known for its next-token prediction paradigm, underpins state-of-the-art language and visual generative models. Traditionally, a ``token'' is treated as the smallest prediction unit, often a discrete symbol in language or a quantized patch in vision. However, the optimal token definition for 2D image structures remains an open question. Moreover, AR models suffer from exposure bias, where teacher forcing during training leads to error accumulation at inference. In this paper, we propose xAR, a generalized AR framework that extends the notion of a token to an entity X, which can represent an individual patch token, a cell (a ktimes k grouping of neighboring patches), a subsample (a non-local grouping of distant patches), a scale (coarse-to-fine resolution), or even a whole image. Additionally, we reformulate discrete token classification as continuous entity regression, leveraging flow-matching methods at each AR step. This approach conditions training on noisy entities instead of ground truth tokens, leading to Noisy Context Learning, which effectively alleviates exposure bias. As a result, xAR offers two key advantages: (1) it enables flexible prediction units that capture different contextual granularity and spatial structures, and (2) it mitigates exposure bias by avoiding reliance on teacher forcing. On ImageNet-256 generation benchmark, our base model, xAR-B (172M), outperforms DiT-XL/SiT-XL (675M) while achieving 20times faster inference. Meanwhile, xAR-H sets a new state-of-the-art with an FID of 1.24, running 2.2times faster than the previous best-performing model without relying on vision foundation modules (\eg, DINOv2) or advanced guidance interval sampling.

Diffusion models have emerged as a powerful paradigm for modern generative modeling, demonstrating strong potential for large language models (LLMs). Unlike conventional autoregressive (AR) models that generate tokens sequentially, diffusion models enable parallel token sampling, leading to faster generation and eliminating left-to-right generation constraints. Despite their empirical success, the theoretical understanding of diffusion model approaches remains underdeveloped. In this work, we develop convergence guarantees for diffusion language models from an information-theoretic perspective. Our analysis demonstrates that the sampling error, measured by the Kullback-Leibler (KL) divergence, decays inversely with the number of iterations T and scales linearly with the mutual information between tokens in the target text sequence. In particular, we establish matching upper and lower bounds, up to some constant factor, to demonstrate the tightness of our convergence analysis. These results offer novel theoretical insights into the practical effectiveness of diffusion language models.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Knowledge-intensive language tasks require NLP systems to both provide the correct answer and retrieve supporting evidence for it in a given corpus. Autoregressive language models are emerging as the de-facto standard for generating answers, with newer and more powerful systems emerging at an astonishing pace. In this paper we argue that all this (and future) progress can be directly applied to the retrieval problem with minimal intervention to the models' architecture. Previous work has explored ways to partition the search space into hierarchical structures and retrieve documents by autoregressively generating their unique identifier. In this work we propose an alternative that doesn't force any structure in the search space: using all ngrams in a passage as its possible identifiers. This setup allows us to use an autoregressive model to generate and score distinctive ngrams, that are then mapped to full passages through an efficient data structure. Empirically, we show this not only outperforms prior autoregressive approaches but also leads to an average improvement of at least 10 points over more established retrieval solutions for passage-level retrieval on the KILT benchmark, establishing new state-of-the-art downstream performance on some datasets, while using a considerably lighter memory footprint than competing systems. Code and pre-trained models at https://github.com/facebookresearch/SEAL.

Masked diffusion language models (MDLMs) have recently emerged as a promising alternative to autoregressive (AR) language models, offering properties such as parallel decoding, flexible generation orders, and the potential for fewer inference steps. Despite these advantages, decoding strategies and reinforcement learning (RL) algorithms tailored for MDLMs remain underexplored. A naive approach is to directly transfer techniques well-established for AR models to MDLMs. However, this raises an immediate question: Is such a naive transfer truly optimal? For example, 1) Block-wise and semi-AR decoding strategies are not employed during the training of MDLMs, so why do they outperform full diffusion-style decoding during inference? 2) Applying RL algorithms designed for AR models directly to MDLMs exhibits a training-inference inconsistency, since MDLM decoding are non-causal (parallel). This results in inconsistencies between the rollout trajectory and the optimization trajectory. To address these challenges, we propose EOS Early Rejection (EOSER) and Ascending Step-Size (ASS) decoding scheduler, which unlock the potential of MDLMs to perform full diffusion-style decoding, achieving competitive performance with fewer decoding steps. Additionally, we introduce Consistency Trajectory Group Relative Policy Optimization (CJ-GRPO) for taming MDLMs, which emphasizes the consistency between rollout trajectory and optimization trajectory, and reduces the optimization errors caused by skip-step optimization. We conduct extensive experiments on reasoning tasks, such as mathematical and planning benchmarks, using LLaDA-8B-Instruct. The results demonstrate that the proposed EOSER and ASS mechanisms, together with CJ-GRPO, hold significant promise for effectively and efficiently taming MDLMs. Code: https://github.com/yjyddq/EOSER-ASS-RL.

Diffusion language models offer parallel token generation and inherent bidirectionality, promising more efficient and powerful sequence modeling compared to autoregressive approaches. However, state-of-the-art diffusion models (e.g., Dream 7B, LLaDA 8B) suffer from slow inference. While they match the quality of similarly sized Autoregressive (AR) Models (e.g., Qwen2.5 7B, Llama3 8B), their iterative denoising requires multiple full-sequence forward passes, resulting in high computational costs and latency, particularly for long input prompts and long-context scenarios. Furthermore, parallel token generation introduces token incoherence problems, and current sampling heuristics suffer from significant quality drops with decreasing denoising steps. We address these limitations with two training-free techniques. First, we propose FreeCache, a Key-Value (KV) approximation caching technique that reuses stable KV projections across denoising steps, effectively reducing the computational cost of DLM inference. Second, we introduce Guided Diffusion, a training-free method that uses a lightweight pretrained autoregressive model to supervise token unmasking, dramatically reducing the total number of denoising iterations without sacrificing quality. We conduct extensive evaluations on open-source reasoning benchmarks, and our combined methods deliver up to a 34x end-to-end speedup without compromising accuracy. For the first time, diffusion language models achieve a comparable and even faster latency as the widely adopted autoregressive models. Our work successfully paved the way for scaling up the diffusion language model to a broader scope of applications across different domains.

In arbitrary-order language models, it is an open question how to sample tokens in parallel from the correct joint distribution. With discrete diffusion models, the more tokens they generate in parallel, the less their predicted distributions adhere to the originally learned data distribution, as they rely on a conditional independence assumption that only works with infinitesimally small timesteps. We find that a different class of models, any-subset autoregressive models (AS-ARMs), holds the solution. As implied by the name, AS-ARMs can generate tokens in any order, and in parallel. Moreover, AS-ARMs support parallelized joint probability density estimation, allowing them to correct their own parallel-generated token distributions, via our Any-Subset Speculative Decoding (ASSD) algorithm. ASSD provably enables generation of tokens from the correct joint distribution, with the number of neural network calls upper bounded by the number of tokens predicted. We empirically verify that ASSD speeds up language generation, without sacrificing quality. Furthermore, we provide a mathematically justified scheme for training AS-ARMs for generation, and show that AS-ARMs achieve state-of-the-art performance among sub-200M parameter models on infilling benchmark tasks, and nearly match the performance of models 50X larger on code generation. Our theoretical and empirical results indicate that the once-forgotten AS-ARMs are a promising direction of language modeling.

Tiny Recursive Models (TRMs) have recently demonstrated remarkable performance on ARC-AGI, showing that very small models can compete against large foundation models through a two-step refinement mechanism that updates an internal reasoning state z and the predicted output y. Naturally, such refinement is of interest for any predictor; it is therefore natural to wonder whether the TRM mechanism could be effectively re-adopted in autoregressive models. However, TRMs cannot be simply compared to standard models because they lack causal predictive structures and contain persistent latent states that make it difficult to isolate specific performance gains. In this paper, we propose the Autoregressive TRM and evaluate it on small autoregressive tasks. To understand its efficacy, we propose a suite of models that gradually transform a standard Transformer to a Tiny Autoregressive Recursive Model in a controlled setting that fixes the block design, token stream, and next-token objective. Across compute-matched experiments on character-level algorithmic tasks, we surprisingly find that there are some two-level refinement baselines that show strong performance. Contrary to expectations, we find no reliable performance gains from the full Autoregressive TRM architecture. These results offer potential promise for two-step refinement mechanisms more broadly but caution against investing in the autoregressive TRM-specific model as a fruitful research direction.

This paper presents Randomized AutoRegressive modeling (RAR) for visual generation, which sets a new state-of-the-art performance on the image generation task while maintaining full compatibility with language modeling frameworks. The proposed RAR is simple: during a standard autoregressive training process with a next-token prediction objective, the input sequence-typically ordered in raster form-is randomly permuted into different factorization orders with a probability r, where r starts at 1 and linearly decays to 0 over the course of training. This annealing training strategy enables the model to learn to maximize the expected likelihood over all factorization orders and thus effectively improve the model's capability of modeling bidirectional contexts. Importantly, RAR preserves the integrity of the autoregressive modeling framework, ensuring full compatibility with language modeling while significantly improving performance in image generation. On the ImageNet-256 benchmark, RAR achieves an FID score of 1.48, not only surpassing prior state-of-the-art autoregressive image generators but also outperforming leading diffusion-based and masked transformer-based methods. Code and models will be made available at https://github.com/bytedance/1d-tokenizer

The impact of randomness on model training is poorly understood. How do differences in data order and initialization actually manifest in the model, such that some training runs outperform others or converge faster? Furthermore, how can we interpret the resulting training dynamics and the phase transitions that characterize different trajectories? To understand the effect of randomness on the dynamics and outcomes of neural network training, we train models multiple times with different random seeds and compute a variety of metrics throughout training, such as the L_2 norm, mean, and variance of the neural network's weights. We then fit a hidden Markov model (HMM) over the resulting sequences of metrics. The HMM represents training as a stochastic process of transitions between latent states, providing an intuitive overview of significant changes during training. Using our method, we produce a low-dimensional, discrete representation of training dynamics on grokking tasks, image classification, and masked language modeling. We use the HMM representation to study phase transitions and identify latent "detour" states that slow down convergence.

Autoregressive (AR) vision-language models (VLMs) have long dominated multimodal understanding, reasoning, and graphical user interface (GUI) grounding. Recently, discrete diffusion vision-language models (DVLMs) have shown strong performance in multimodal reasoning, offering bidirectional attention, parallel token generation, and iterative refinement. However, their potential for GUI grounding remains unexplored. In this work, we evaluate whether discrete DVLMs can serve as a viable alternative to AR models for GUI grounding. We adapt LLaDA-V for single-turn action and bounding-box prediction, framing the task as text generation from multimodal input. To better capture the hierarchical structure of bounding-box geometry, we propose a hybrid masking schedule that combines linear and deterministic masking, improving grounding accuracy by up to 6.1 points in Step Success Rate (SSR) over the GUI-adapted LLaDA-V trained with linear masking. Evaluations on four datasets spanning web, desktop, and mobile interfaces show that the adapted diffusion model with hybrid masking consistently outperforms the linear-masked variant and performs competitively with autoregressive counterparts despite limited pretraining. Systematic ablations reveal that increasing diffusion steps, generation length, and block length improves accuracy but also increases latency, with accuracy plateauing beyond a certain number of diffusion steps. Expanding the training data with diverse GUI domains further reduces latency by about 1.3 seconds and improves grounding accuracy by an average of 20 points across benchmarks. These results demonstrate that discrete DVLMs are a promising modeling framework for GUI grounding and represent an important step toward diffusion-based GUI agents.

This paper combines autoregressive and masked-diffusion training objectives without any architectural modifications, resulting in flexible language models that outperform single-objective models. Autoregressive modeling has been a popular approach, partly because of its training efficiency; however, that comes at the cost of sensitivity to overfitting. On the other hand, masked-diffusion models are less efficient to train while being more resilient to overfitting. In this work, we demonstrate that dual-objective training achieves the best of both worlds. To derive the optimal balance between both objectives, we train and evaluate 50 language models under varying levels of data repetition. We show that it is optimal to combine both objectives under all evaluated settings and that the optimal balance is similar whether targeting autoregressive or masked-diffusion downstream performance.

Scene text recognition (STR) methods have struggled to attain high accuracy and fast inference speed. Autoregressive (AR)-based models implement the recognition in a character-by-character manner, showing superiority in accuracy but with slow inference speed. Alternatively, parallel decoding (PD)-based models infer all characters in a single decoding pass, offering faster inference speed but generally worse accuracy. We first present an empirical study of AR decoding in STR, and discover that the AR decoder not only models linguistic context, but also provides guidance on visual context perception. Consequently, we propose Context Perception Parallel Decoder (CPPD) to predict the character sequence in a PD pass. CPPD devises a character counting module to infer the occurrence count of each character, and a character ordering module to deduce the content-free reading order and placeholders. Meanwhile, the character prediction task associates the placeholders with characters. They together build a comprehensive recognition context. We construct a series of CPPD models and also plug the proposed modules into existing STR decoders. Experiments on both English and Chinese benchmarks demonstrate that the CPPD models achieve highly competitive accuracy while running approximately 8x faster than their AR-based counterparts. Moreover, the plugged models achieve significant accuracy improvements. Code is at https://github.com/PaddlePaddle/PaddleOCR/blob/dygraph/doc/doc_en/algorithm_rec_cppd_en.md{this https URL}.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

We present significant extensions to diffusion-based sequence generation models, blurring the line with autoregressive language models. We introduce hyperschedules, which assign distinct noise schedules to individual token positions, generalizing both autoregressive models (e.g., GPT) and conventional diffusion models (e.g., SEDD, MDLM) as special cases. Second, we propose two hybrid token-wise noising processes that interpolate between absorbing and uniform processes, enabling the model to fix past mistakes, and we introduce a novel inference algorithm that leverages this new feature in a simplified context inspired from MDLM. To support efficient training and inference, we design attention masks compatible with KV-caching. Our methods achieve state-of-the-art perplexity and generate diverse, high-quality sequences across standard benchmarks, suggesting a promising path for autoregressive diffusion-based sequence generation.

Autoregressive models (ARMs) are widely regarded as the cornerstone of large language models (LLMs). We challenge this notion by introducing LLaDA, a diffusion model trained from scratch under the pre-training and supervised fine-tuning (SFT) paradigm. LLaDA models distributions through a forward data masking process and a reverse process, parameterized by a vanilla Transformer to predict masked tokens. By optimizing a likelihood bound, it provides a principled generative approach for probabilistic inference. Across extensive benchmarks, LLaDA demonstrates strong scalability, outperforming our self-constructed ARM baselines. Remarkably, LLaDA 8B is competitive with strong LLMs like LLaMA3 8B in in-context learning and, after SFT, exhibits impressive instruction-following abilities in case studies such as multi-turn dialogue. Moreover, LLaDA addresses the reversal curse, surpassing GPT-4o in a reversal poem completion task. Our findings establish diffusion models as a viable and promising alternative to ARMs, challenging the assumption that key LLM capabilities discussed above are inherently tied to ARMs.

In this paper we present a new framework for time-series modeling that combines the best of traditional statistical models and neural networks. We focus on time-series with long-range dependencies, needed for monitoring fine granularity data (e.g. minutes, seconds, milliseconds), prevalent in operational use-cases. Traditional models, such as auto-regression fitted with least squares (Classic-AR) can model time-series with a concise and interpretable model. When dealing with long-range dependencies, Classic-AR models can become intractably slow to fit for large data. Recently, sequence-to-sequence models, such as Recurrent Neural Networks, which were originally intended for natural language processing, have become popular for time-series. However, they can be overly complex for typical time-series data and lack interpretability. A scalable and interpretable model is needed to bridge the statistical and deep learning-based approaches. As a first step towards this goal, we propose modelling AR-process dynamics using a feed-forward neural network approach, termed AR-Net. We show that AR-Net is as interpretable as Classic-AR but also scales to long-range dependencies. Our results lead to three major conclusions: First, AR-Net learns identical AR-coefficients as Classic-AR, thus being equally interpretable. Second, the computational complexity with respect to the order of the AR process, is linear for AR-Net as compared to a quadratic for Classic-AR. This makes it possible to model long-range dependencies within fine granularity data. Third, by introducing regularization, AR-Net automatically selects and learns sparse AR-coefficients. This eliminates the need to know the exact order of the AR-process and allows to learn sparse weights for a model with long-range dependencies.

Generative recommendation (GR) typically first quantizes continuous item embeddings into multi-level semantic IDs (SIDs), and then generates the next item via autoregressive decoding. Although existing methods are already competitive in terms of recommendation performance, directly inheriting the autoregressive decoding paradigm from language models still suffers from three key limitations: (1) autoregressive decoding struggles to jointly capture global dependencies among the multi-dimensional features associated with different positions of SID; (2) using a unified, fixed decoding path for the same item implicitly assumes that all users attend to item attributes in the same order; (3) autoregressive decoding is inefficient at inference time and struggles to meet real-time requirements. To tackle these challenges, we propose MDGR, a Masked Diffusion Generative Recommendation framework that reshapes the GR pipeline from three perspectives: codebook, training, and inference. (1) We adopt a parallel codebook to provide a structural foundation for diffusion-based GR. (2) During training, we adaptively construct masking supervision signals along both the temporal and sample dimensions. (3) During inference, we develop a warm-up-based two-stage parallel decoding strategy for efficient generation of SIDs. Extensive experiments on multiple public and industrial-scale datasets show that MDGR outperforms ten state-of-the-art baselines by up to 10.78%. Furthermore, by deploying MDGR on a large-scale online advertising platform, we achieve a 1.20% increase in revenue, demonstrating its practical value.

Real-world perception and interaction are inherently multimodal, encompassing not only language but also vision and speech, which motivates the development of "Omni" MLLMs that support both multimodal inputs and multimodal outputs. While a sequence of omni MLLMs has emerged, most existing systems still rely on additional expert components to achieve multimodal generation, limiting the simplicity of unified training and inference. Autoregressive (AR) modeling, with a single token stream, a single next-token objective, and a single decoder, is an elegant and scalable foundation in the text domain. Motivated by this, we present AR-Omni, a unified any-to-any model in the autoregressive paradigm without any expert decoders. AR-Omni supports autoregressive text and image generation, as well as streaming speech generation, all under a single Transformer decoder. We further address three practical issues in unified AR modeling: modality imbalance via task-aware loss reweighting, visual fidelity via a lightweight token-level perceptual alignment loss for image tokens, and stability-creativity trade-offs via a finite-state decoding mechanism. Empirically, AR-Omni achieves strong quality across three modalities while remaining real-time, achieving a 0.88 real-time factor for speech generation.

Despite remarkable progress in autoregressive language models, alternative generative paradigms beyond left-to-right generation are still being actively explored. Discrete diffusion models, with the capacity for parallel generation, have recently emerged as a promising alternative. Unfortunately, these models still underperform the autoregressive counterparts, with the performance gap increasing when reducing the number of sampling steps. Our analysis reveals that this degradation is a consequence of an imperfect approximation used by diffusion models. In this work, we propose Energy-based Diffusion Language Model (EDLM), an energy-based model operating at the full sequence level for each diffusion step, introduced to improve the underlying approximation used by diffusion models. More specifically, we introduce an EBM in a residual form, and show that its parameters can be obtained by leveraging a pretrained autoregressive model or by finetuning a bidirectional transformer via noise contrastive estimation. We also propose an efficient generation algorithm via parallel important sampling. Comprehensive experiments on language modeling benchmarks show that our model can consistently outperform state-of-the-art diffusion models by a significant margin, and approaches autoregressive models' perplexity. We further show that, without any generation performance drop, our framework offers a 1.3times sampling speedup over existing diffusion models.

Autoregressive decoding in Large Language Models (LLMs) is inherently sequential, creating a latency bottleneck that scales linearly with output length. While ``Decomposition-and-Fill'' methods like Skeleton-of-Thought attempt to parallelize generation via external orchestration, they suffer from coherence drift due to the lack of cross-stream communication. In this work, we introduce the Parallel Decoder Transformer (PDT), a parameter-efficient architecture that embeds coordination primitives directly into the inference process of a frozen pre-trained model. Instead of retraining the base model, PDT injects lightweight Speculative Note Conditioning (SNC) adapters that allow parallel decoding streams to synchronize via a shared, dynamic latent space. We formulate coordination as a speculative consensus problem, where sibling streams broadcast semantic ``notes'' to a global bus, gated by a learned verification head. We validate our approach on a 50,000-step curriculum using a frozen 20B-parameter backbone. Our results demonstrate that PDT achieves effective self-correction, reaching 77.8\% precision in coverage prediction and recovering approximate serial semantics without modifying the trunk weights. This establishes PDT as a scalable, efficient alternative to full model fine-tuning for structured parallel generation.

Masked autoregressive models (MAR) have recently emerged as a powerful paradigm for image and video generation, combining the flexibility of masked modeling with the potential of continuous tokenizer. However, video MAR models suffer from two major limitations: the slow-start problem, caused by the lack of a structured global prior at early sampling stages, and error accumulation across the autoregression in both spatial and temporal dimensions. In this work, we propose CanvasMAR, a novel video MAR model that mitigates these issues by introducing a canvas mechanism--a blurred, global prediction of the next frame, used as the starting point for masked generation. The canvas provides global structure early in sampling, enabling faster and more coherent frame synthesis. Furthermore, we introduce compositional classifier-free guidance that jointly enlarges spatial (canvas) and temporal conditioning, and employ noise-based canvas augmentation to enhance robustness. Experiments on the BAIR and Kinetics-600 benchmarks demonstrate that CanvasMAR produces high-quality videos with fewer autoregressive steps. Our approach achieves remarkable performance among autoregressive models on Kinetics-600 dataset and rivals diffusion-based methods.

We explore deep autoregressive Transformer models in language modeling for speech recognition. We focus on two aspects. First, we revisit Transformer model configurations specifically for language modeling. We show that well configured Transformer models outperform our baseline models based on the shallow stack of LSTM recurrent neural network layers. We carry out experiments on the open-source LibriSpeech 960hr task, for both 200K vocabulary word-level and 10K byte-pair encoding subword-level language modeling. We apply our word-level models to conventional hybrid speech recognition by lattice rescoring, and the subword-level models to attention based encoder-decoder models by shallow fusion. Second, we show that deep Transformer language models do not require positional encoding. The positional encoding is an essential augmentation for the self-attention mechanism which is invariant to sequence ordering. However, in autoregressive setup, as is the case for language modeling, the amount of information increases along the position dimension, which is a positional signal by its own. The analysis of attention weights shows that deep autoregressive self-attention models can automatically make use of such positional information. We find that removing the positional encoding even slightly improves the performance of these models.

Autoregressive Large Language Models have transformed the landscape of Natural Language Processing. Pre-train and prompt paradigm has replaced the conventional approach of pre-training and fine-tuning for many downstream NLP tasks. This shift has been possible largely due to LLMs and innovative prompting techniques. LLMs have shown great promise for a variety of downstream tasks owing to their vast parameters and huge datasets that they are pre-trained on. However, in order to fully realize their potential, their outputs must be guided towards the desired outcomes. Prompting, in which a specific input or instruction is provided to guide the LLMs toward the intended output, has become a tool for achieving this goal. In this paper, we discuss the various prompting techniques that have been applied to fully harness the power of LLMs. We present a taxonomy of existing literature on prompting techniques and provide a concise survey based on this taxonomy. Further, we identify some open problems in the realm of prompting in autoregressive LLMs which could serve as a direction for future research.

Time series analysis has witnessed the inspiring development from traditional autoregressive models, deep learning models, to recent Transformers and Large Language Models (LLMs). Efforts in leveraging vision models for time series analysis have also been made along the way but are less visible to the community due to the predominant research on sequence modeling in this domain. However, the discrepancy between continuous time series and the discrete token space of LLMs, and the challenges in explicitly modeling the correlations of variates in multivariate time series have shifted some research attentions to the equally successful Large Vision Models (LVMs) and Vision Language Models (VLMs). To fill the blank in the existing literature, this survey discusses the advantages of vision models over LLMs in time series analysis. It provides a comprehensive and in-depth overview of the existing methods, with dual views of detailed taxonomy that answer the key research questions including how to encode time series as images and how to model the imaged time series for various tasks. Additionally, we address the challenges in the pre- and post-processing steps involved in this framework and outline future directions to further advance time series analysis with vision models.

In autoregressive (AR) image generation, models based on the 'next-token prediction' paradigm of LLMs have shown comparable performance to diffusion models by reducing inductive biases. However, directly applying LLMs to complex image generation can struggle with reconstructing the image's structure and details, impacting the generation's accuracy and stability. Additionally, the 'next-token prediction' paradigm in the AR model does not align with the contextual scanning and logical reasoning processes involved in human visual perception, limiting effective image generation. Prompt engineering, as a key technique for guiding LLMs, leverages specifically designed prompts to improve model performance on complex natural language processing (NLP) tasks, enhancing accuracy and stability of generation while maintaining contextual coherence and logical consistency, similar to human reasoning. Inspired by prompt engineering from the field of NLP, we propose Vision Full-view prompt (VF prompt) to enhance autoregressive image generation. Specifically, we design specialized image-related VF prompts for AR image generation to simulate the process of human image creation. This enhances contextual logic ability by allowing the model to first perceive overall distribution information before generating the image, and improve generation stability by increasing the inference steps. Compared to the AR method without VF prompts, our method shows outstanding performance and achieves an approximate improvement of 20%.

Autoregressive language models (ARMs) deliver strong likelihoods, but are inherently serial: they generate one token per forward pass, which limits throughput and inflates latency for long sequences. Diffusion Language Models (DLMs) parallelize across positions and thus appear promising for language generation, yet standard discrete diffusion typically needs hundreds to thousands of model evaluations to reach high quality, trading serial depth for iterative breadth. We introduce FS-DFM, Few-Step Discrete Flow-Matching. A discrete flow-matching model designed for speed without sacrificing quality. The core idea is simple: make the number of sampling steps an explicit parameter and train the model to be consistent across step budgets, so one big move lands where many small moves would. We pair this with a reliable update rule that moves probability in the right direction without overshooting, and with strong teacher guidance distilled from long-run trajectories. Together, these choices make few-step sampling stable, accurate, and easy to control. On language modeling benchmarks, FS-DFM with 8 sampling steps achieves perplexity parity with a 1,024-step discrete-flow baseline for generating 1,024 tokens using a similar-size model, delivering up to 128 times faster sampling and corresponding latency/throughput gains.

Despite the crucial importance of accelerating text generation in large language models (LLMs) for efficiently producing content, the sequential nature of this process often leads to high inference latency, posing challenges for real-time applications. Various techniques have been proposed and developed to address these challenges and improve efficiency. This paper presents a comprehensive survey of accelerated generation techniques in autoregressive language models, aiming to understand the state-of-the-art methods and their applications. We categorize these techniques into several key areas: speculative decoding, early exiting mechanisms, and non-autoregressive methods. We discuss each category's underlying principles, advantages, limitations, and recent advancements. Through this survey, we aim to offer insights into the current landscape of techniques in LLMs and provide guidance for future research directions in this critical area of natural language processing.

Despite a growing interest in diffusion-based language models, existing work has not shown that these models can attain nontrivial likelihoods on standard language modeling benchmarks. In this work, we take the first steps towards closing the likelihood gap between autoregressive and diffusion-based language models, with the goal of building and releasing a diffusion model which outperforms a small but widely-known autoregressive model. We pursue this goal through algorithmic improvements, scaling laws, and increased compute. On the algorithmic front, we introduce several methodological improvements for the maximum-likelihood training of diffusion language models. We then study scaling laws for our diffusion models and find compute-optimal training regimes which differ substantially from autoregressive models. Using our methods and scaling analysis, we train and release Plaid 1B, a large diffusion language model which outperforms GPT-2 124M in likelihood on benchmark datasets and generates fluent samples in unconditional and zero-shot control settings.

Autoregressive (AR) models have emerged as powerful tools for image generation by modeling images as sequences of discrete tokens. While Classifier-Free Guidance (CFG) has been adopted to improve conditional generation, its application in AR models faces two key issues: guidance diminishing, where the conditional-unconditional gap quickly vanishes as decoding progresses, and over-guidance, where strong conditions distort visual coherence. To address these challenges, we propose SoftCFG, an uncertainty-guided inference method that distributes adaptive perturbations across all tokens in the sequence. The key idea behind SoftCFG is to let each generated token contribute certainty-weighted guidance, ensuring that the signal persists across steps while resolving conflicts between text guidance and visual context. To further stabilize long-sequence generation, we introduce Step Normalization, which bounds cumulative perturbations of SoftCFG. Our method is training-free, model-agnostic, and seamlessly integrates with existing AR pipelines. Experiments show that SoftCFG significantly improves image quality over standard CFG and achieves state-of-the-art FID on ImageNet 256*256 among autoregressive models.

Conventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity for autoregressive modeling. In this work, we propose to model the per-token probability distribution using a diffusion procedure, which allows us to apply autoregressive models in a continuous-valued space. Rather than using categorical cross-entropy loss, we define a Diffusion Loss function to model the per-token probability. This approach eliminates the need for discrete-valued tokenizers. We evaluate its effectiveness across a wide range of cases, including standard autoregressive models and generalized masked autoregressive (MAR) variants. By removing vector quantization, our image generator achieves strong results while enjoying the speed advantage of sequence modeling. We hope this work will motivate the use of autoregressive generation in other continuous-valued domains and applications.

Non-linear state-space models, also known as general hidden Markov models, are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences in general. The particle-based, rapid incremental smoother PaRIS is a sequential Monte Carlo (SMC) technique allowing for efficient online approximation of expectations of additive functionals under the smoothing distribution in these models. Such expectations appear naturally in several learning contexts, such as likelihood estimation (MLE) and Markov score climbing (MSC). PARIS has linear computational complexity, limited memory requirements and comes with non-asymptotic bounds, convergence results and stability guarantees. Still, being based on self-normalised importance sampling, the PaRIS estimator is biased. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs PPG sampler, which can be viewed as a PaRIS algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. Our second contribution is to apply PPG in a learning framework, covering MLE and MSC as special examples. In this context, we establish, under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao--Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.

Unified generation of sequence and structure for scientific data (e.g., materials, molecules, proteins) is a critical task. Existing approaches primarily rely on either autoregressive sequence models or diffusion models, each offering distinct advantages and facing notable limitations. Autoregressive models, such as GPT, Llama, and Phi-4, have demonstrated remarkable success in natural language generation and have been extended to multimodal tasks (e.g., image, video, and audio) using advanced encoders like VQ-VAE to represent complex modalities as discrete sequences. However, their direct application to scientific domains is challenging due to the high precision requirements and the diverse nature of scientific data. On the other hand, diffusion models excel at generating high-dimensional scientific data, such as protein, molecule, and material structures, with remarkable accuracy. Yet, their inability to effectively model sequences limits their potential as general-purpose multimodal foundation models. To address these challenges, we propose UniGenX, a unified framework that combines autoregressive next-token prediction with conditional diffusion models. This integration leverages the strengths of autoregressive models to ease the training of conditional diffusion models, while diffusion-based generative heads enhance the precision of autoregressive predictions. We validate the effectiveness of UniGenX on material and small molecule generation tasks, achieving a significant leap in state-of-the-art performance for material crystal structure prediction and establishing new state-of-the-art results for small molecule structure prediction, de novo design, and conditional generation. Notably, UniGenX demonstrates significant improvements, especially in handling long sequences for complex structures, showcasing its efficacy as a versatile tool for scientific data generation.

Autoregressive (AR) language modeling is the dominant paradigm for text generation, yet its sequential token-by-token decoding makes inference memory-bound and inefficient. Existing acceleration approaches, such as speculative decoding and diffusion language models, can yield speedups under certain conditions but do not directly address high-load batch serving--the scenario most critical for industrial-scale deployment. We introduce K-Forcing, a push-forward language modeling paradigm for joint next-k-token decoding. K-Forcing distills an existing AR model into a conditional push-forward mapping--one that transforms independent uniform noise variables into a joint sample of multiple future tokens in a single forward pass. This design preserves fixed-length outputs, reuses the AR teacher backbone, and remains compatible with standard AR serving infrastructure. We train this mapping via progressive self-forcing distillation, which gradually expands the prediction window while enabling the student to closely match the sequence distribution of the AR teacher. We evaluate K-Forcing on LM1B and OpenWebText using a standard causal Transformer backbone. When aggressively configured to generate k = 4 tokens per forward pass, K-Forcing delivers approximately 2.4-3.5x speedup across different batch sizes, while incurring modest quality degradation relative to its AR teacher. As inference increasingly dominates the lifetime compute cost of modern LLMs, K-Forcing offers a promising route toward accelerating AR generation under real-world high-load deployment.

Self-supervised speech representations have been shown to be effective in a variety of speech applications. However, existing representation learning methods generally rely on the autoregressive model and/or observed global dependencies while generating the representation. In this work, we propose Non-Autoregressive Predictive Coding (NPC), a self-supervised method, to learn a speech representation in a non-autoregressive manner by relying only on local dependencies of speech. NPC has a conceptually simple objective and can be implemented easily with the introduced Masked Convolution Blocks. NPC offers a significant speedup for inference since it is parallelizable in time and has a fixed inference time for each time step regardless of the input sequence length. We discuss and verify the effectiveness of NPC by theoretically and empirically comparing it with other methods. We show that the NPC representation is comparable to other methods in speech experiments on phonetic and speaker classification while being more efficient.

Existing autoregressive (AR) image generative models use a token-by-token generation schema. That is, they predict a per-token probability distribution and sample the next token from that distribution. The main challenge is how to model the complex distribution of high-dimensional tokens. Previous methods either are too simplistic to fit the distribution or result in slow generation speed. Instead of fitting the distribution of the whole tokens, we explore using a AR model to generate each token in a feature-by-feature way, i.e., taking the generated features as input and generating the next feature. Based on that, we propose ARINAR (AR-in-AR), a bi-level AR model. The outer AR layer take previous tokens as input, predicts a condition vector z for the next token. The inner layer, conditional on z, generates features of the next token autoregressively. In this way, the inner layer only needs to model the distribution of a single feature, for example, using a simple Gaussian Mixture Model. On the ImageNet 256x256 image generation task, ARINAR-B with 213M parameters achieves an FID of 2.75, which is comparable to the state-of-the-art MAR-B model (FID=2.31), while five times faster than the latter.

Autoregressive Predictive Coding (APC), as a self-supervised objective, has enjoyed success in learning representations from large amounts of unlabeled data, and the learned representations are rich for many downstream tasks. However, the connection between low self-supervised loss and strong performance in downstream tasks remains unclear. In this work, we propose Vector-Quantized Autoregressive Predictive Coding (VQ-APC), a novel model that produces quantized representations, allowing us to explicitly control the amount of information encoded in the representations. By studying a sequence of increasingly limited models, we reveal the constituents of the learned representations. In particular, we confirm the presence of information with probing tasks, while showing the absence of information with mutual information, uncovering the model's preference in preserving speech information as its capacity becomes constrained. We find that there exists a point where phonetic and speaker information are amplified to maximize a self-supervised objective. As a byproduct, the learned codes for a particular model capacity correspond well to English phones.

Large language model (LLM) decoding involves generating a sequence of tokens based on a given context, where each token is predicted one at a time using the model's learned probabilities. The typical autoregressive decoding method requires a separate forward pass through the model for each token generated, which is computationally inefficient and poses challenges for deploying LLMs in latency-sensitive scenarios. The main limitations of current decoding methods stem from their inefficiencies and resource demands. Existing approaches either necessitate fine-tuning smaller models, which is resource-intensive, or rely on fixed retrieval schemes to construct drafts for the next tokens, which lack adaptability and fail to generalize across different models and contexts. To address these issues, we introduce a novel methodology called ADED, which accelerates LLM decoding without requiring fine-tuning. Our approach involves an adaptive draft-verification process that evolves over time to improve efficiency. We utilize a tri-gram matrix-based LLM representation to dynamically approximate the output distribution of the LLM, allowing the model to adjust to changing token probabilities during the decoding process. Additionally, we implement a draft construction mechanism that effectively balances exploration and exploitation, ensuring that the drafts generated are both diverse and close to the true output distribution of the LLM. The importance of this design lies in its ability to optimize the draft distribution adaptively, leading to faster and more accurate decoding. Through extensive experiments on various benchmark datasets and LLM architectures, we demonstrate that ADED significantly accelerates the decoding process while maintaining high accuracy, making it suitable for deployment in a wide range of practical applications.

While autoregressive (AR) LLM-based ASR systems achieve strong accuracy, their sequential decoding limits parallelism and incurs high latency. We propose NLE, a non-autoregressive (NAR) approach that formulates speech recognition as conditional transcript editing, enabling fully parallel prediction. NLE extracts acoustic embeddings and an initial hypothesis from a pretrained speech encoder, then refines the hypothesis using a bidirectional LLM editor trained with a latent alignment objective. An interleaved padding strategy exploits the identity mapping bias of Transformers, allowing the model to focus on corrections rather than full reconstruction. On the Open ASR leaderboard, NLE++ achieves 5.67% average WER with an RTFx (inverse real-time factor) of 1630. In single-utterance scenarios, NLE achieves 27x speedup over the AR baseline, making it suitable for real-time applications.

This report presents PixelBytes, an approach for unified multimodal representation learning. Drawing inspiration from sequence models like Image Transformers, PixelCNN, and Mamba-Bytes, we explore integrating text, audio, action-state, and pixelated images (sprites) into a cohesive representation. We conducted experiments on a PixelBytes Pokemon dataset and an Optimal-Control dataset. Our investigation covered various model architectures, including Recurrent Neural Networks (RNNs), State Space Models (SSMs), and Attention-based models, with a focus on bidirectional processing and our PxBy embedding technique. We evaluated models based on data reduction strategies and autoregressive learning, specifically examining Long Short-Term Memory (LSTM) networks in predictive and autoregressive modes. Our results indicate that autoregressive models perform better than predictive models in this context. Additionally, we found that diffusion models can be applied to control problems and parallelized generation. PixelBytes aims to contribute to the development of foundation models for multimodal data processing and generation. The project's code, models, and datasets are available online.

Masked-based autoregressive models have demonstrated promising image generation capability in continuous space. However, their potential for video generation remains under-explored. In this paper, we propose VideoMAR, a concise and efficient decoder-only autoregressive image-to-video model with continuous tokens, composing temporal frame-by-frame and spatial masked generation. We first identify temporal causality and spatial bi-directionality as the first principle of video AR models, and propose the next-frame diffusion loss for the integration of mask and video generation. Besides, the huge cost and difficulty of long sequence autoregressive modeling is a basic but crucial issue. To this end, we propose the temporal short-to-long curriculum learning and spatial progressive resolution training, and employ progressive temperature strategy at inference time to mitigate the accumulation error. Furthermore, VideoMAR replicates several unique capacities of language models to video generation. It inherently bears high efficiency due to simultaneous temporal-wise KV cache and spatial-wise parallel generation, and presents the capacity of spatial and temporal extrapolation via 3D rotary embeddings. On the VBench-I2V benchmark, VideoMAR surpasses the previous state-of-the-art (Cosmos I2V) while requiring significantly fewer parameters (9.3%), training data (0.5%), and GPU resources (0.2%).

Essential to visual generation is efficient modeling of visual data priors. Conventional next-token prediction methods define the process as learning the conditional probability distribution of successive tokens. Recently, next-scale prediction methods redefine the process to learn the distribution over multi-scale representations, significantly reducing generation latency. However, these methods condition each scale on all previous scales and require each token to consider all preceding tokens, exhibiting scale and spatial redundancy. To better model the distribution by mitigating redundancy, we propose Markovian Visual AutoRegressive modeling (MVAR), a novel autoregressive framework that introduces scale and spatial Markov assumptions to reduce the complexity of conditional probability modeling. Specifically, we introduce a scale-Markov trajectory that only takes as input the features of adjacent preceding scale for next-scale prediction, enabling the adoption of a parallel training strategy that significantly reduces GPU memory consumption. Furthermore, we propose spatial-Markov attention, which restricts the attention of each token to a localized neighborhood of size k at corresponding positions on adjacent scales, rather than attending to every token across these scales, for the pursuit of reduced modeling complexity. Building on these improvements, we reduce the computational complexity of attention calculation from O(N^2) to O(Nk), enabling training with just eight NVIDIA RTX 4090 GPUs and eliminating the need for KV cache during inference. Extensive experiments on ImageNet demonstrate that MVAR achieves comparable or superior performance with both small model trained from scratch and large fine-tuned models, while reducing the average GPU memory footprint by 3.0x.

Autoregressive (AR) models for image generation typically adopt a two-stage paradigm of vector quantization and raster-scan ``next-token prediction", inspired by its great success in language modeling. However, due to the huge modality gap, image autoregressive models may require a systematic reevaluation from two perspectives: tokenizer format and regression direction. In this paper, we introduce the frequency progressive autoregressive (FAR) paradigm and instantiate FAR with the continuous tokenizer. Specifically, we identify spectral dependency as the desirable regression direction for FAR, wherein higher-frequency components build upon the lower one to progressively construct a complete image. This design seamlessly fits the causality requirement for autoregressive models and preserves the unique spatial locality of image data. Besides, we delve into the integration of FAR and the continuous tokenizer, introducing a series of techniques to address optimization challenges and improve the efficiency of training and inference processes. We demonstrate the efficacy of FAR through comprehensive experiments on the ImageNet dataset and verify its potential on text-to-image generation.

The success of autoregressive (AR) language models in text generation has inspired the computer vision community to adopt Large Language Models (LLMs) for image generation. However, considering the essential differences between text and image modalities, the design space of language models for image generation remains underexplored. We observe that image tokens exhibit greater randomness compared to text tokens, which presents challenges when training with token prediction. Nevertheless, AR models demonstrate their potential by effectively learning patterns even from a seemingly suboptimal optimization problem. Our analysis also reveals that while all models successfully grasp the importance of local information in image generation, smaller models struggle to capture the global context. In contrast, larger models showcase improved capabilities in this area, helping to explain the performance gains achieved when scaling up model size. We further elucidate the design space of language models for vision generation, including tokenizer choice, model choice, model scalability, vocabulary design, and sampling strategy through extensive comparative experiments. Our work is the first to analyze the optimization behavior of language models in vision generation, and we believe it can inspire more effective designs when applying LMs to other domains. Finally, our elucidated language model for image generation, termed as ELM, achieves state-of-the-art performance on the ImageNet 256*256 benchmark. The code is available at https://github.com/Pepperlll/LMforImageGeneration.git.

This research aims to accelerate the inference speed of large language models (LLMs) with billions of parameters. We propose Smart Parallel Auto-Correct dEcoding (SPACE), an innovative approach designed for achieving lossless acceleration of LLMs. By integrating semi-autoregressive inference and speculative decoding capabilities, SPACE uniquely enables autoregressive LLMs to parallelize token generation and verification. This is realized through a specialized semi-autoregressive supervised fine-tuning process that equips existing LLMs with the ability to simultaneously predict multiple tokens. Additionally, an auto-correct decoding algorithm facilitates the simultaneous generation and verification of token sequences within a single model invocation. Through extensive experiments on a range of LLMs, SPACE has demonstrated inference speedup ranging from 2.7x-4.0x on HumanEval-X while maintaining output quality.

Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, they are often treated as black-box models and as such it is difficult to understand what exactly they learn as well as how they arrive at a particular prediction. Second, they tend to work poorly on sequences requiring long-term memorization, despite having this capacity in principle. We aim to address both shortcomings with a class of recurrent networks that use a stochastic state transition mechanism between cell applications. This mechanism, which we term state-regularization, makes RNNs transition between a finite set of learnable states. We evaluate state-regularized RNNs on (1) regular languages for the purpose of automata extraction; (2) non-regular languages such as balanced parentheses and palindromes where external memory is required; and (3) real-word sequence learning tasks for sentiment analysis, visual object recognition and text categorisation. We show that state-regularization (a) simplifies the extraction of finite state automata that display an RNN's state transition dynamic; (b) forces RNNs to operate more like automata with external memory and less like finite state machines, which potentiality leads to a more structural memory; (c) leads to better interpretability and explainability of RNNs by leveraging the probabilistic finite state transition mechanism over time steps.

While diffusion models excel at generating high-quality images, prior work reports a significant performance gap between diffusion and autoregressive (AR) methods in language modeling. In this work, we show that simple masked discrete diffusion is more performant than previously thought. We apply an effective training recipe that improves the performance of masked diffusion models and derive a simplified, Rao-Blackwellized objective that results in additional improvements. Our objective has a simple form -- it is a mixture of classical masked language modeling losses -- and can be used to train encoder-only language models that admit efficient samplers, including ones that can generate arbitrary lengths of text semi-autoregressively like a traditional language model. On language modeling benchmarks, a range of masked diffusion models trained with modern engineering practices achieves a new state-of-the-art among diffusion models, and approaches AR perplexity. We release our code at: https://github.com/kuleshov-group/mdlm

Large language models (LLMs) have demonstrated remarkable capabilities in numerous real-world applications. While the vast majority of research conducted from an experimental perspective is progressing rapidly, it demands substantial computational power, data, and other resources. Therefore, how to open the black-box of LLMs from a theoretical standpoint has become a critical challenge. This paper takes the theory of rate-distortion function, directed information, and Granger causality as its starting point to investigate the information-theoretic principles behind LLMs, leading to the development of semantic information theory for LLMs, where the fundamental unit is token, rather than bits that lacks any semantic meaning. By defining the probabilistic model of LLMs, we discuss structure-agnostic information-theoretic measures, such as the directed rate-distortion function in pre-training, the directed rate-reward function in post-training, and the semantic information flow in inference phase. This paper also delves deeply into the theory of token-level semantic embedding and the information-theoretically optimal vectorization method. Thereafter, we propose a general definition of autoregression LLM, where the Transformer architecture and its performance such as ELBO, generalization error bound, memory capacity, and semantic information measures can be derived theoretically. Other architectures, such as Mamba/Mamba2 and LLaDA, are also discussed in our framework. Consequently, this paper provides a theoretical framework for understanding LLMs from the perspective of semantic information theory, which also offers the necessary theoretical tools for further in-depth research.

Autoregressive Large Language Models (e.g., LLaMa, GPTs) are omnipresent achieving remarkable success in language understanding and generation. However, such impressive capability typically comes with a substantial model size, which presents significant challenges for autoregressive token-by-token generation. To mitigate computation overload incurred during generation, several early-exit and layer-dropping strategies have been proposed. Despite some promising success due to the redundancy across LLMs layers on metrics like Rough-L/BLUE, our careful knowledge-intensive evaluation unveils issues such as generation collapse, hallucination of wrong facts, and noticeable performance drop even at the trivial exit ratio of 10-15% of layers. We attribute these errors primarily to ineffective handling of the KV cache through state copying during early-exit. In this work, we observed the saturation of computationally expensive feed-forward blocks of LLM layers and proposed FFN-SkipLLM, which is a novel fine-grained skip strategy of autoregressive LLMs. More specifically, FFN-SkipLLM is an input-adaptive feed-forward skipping strategy that can skip 25-30% of FFN blocks of LLMs with marginal change in performance on knowledge-intensive generation tasks without any requirement to handle KV cache. Our extensive experiments and ablation across benchmarks like MT-Bench, Factoid-QA, and variable-length text summarization illustrate how our simple and ease-at-use method can facilitate faster autoregressive decoding.

Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Autoregressive Transformers adopted in Large Language Models (LLMs) are hard to scale to long sequences. Despite several works trying to reduce their computational cost, most of LLMs still adopt attention layers between all pairs of tokens in the sequence, thus incurring a quadratic cost. In this study, we present a novel approach that dynamically prunes contextual information while preserving the model's expressiveness, resulting in reduced memory and computational requirements during inference. Our method employs a learnable mechanism that determines which uninformative tokens can be dropped from the context at any point across the generation process. By doing so, our approach not only addresses performance concerns but also enhances interpretability, providing valuable insight into the model's decision-making process. Our technique can be applied to existing pre-trained models through a straightforward fine-tuning process, and the pruning strength can be specified by a sparsity parameter. Notably, our empirical findings demonstrate that we can effectively prune up to 80\% of the context without significant performance degradation on downstream tasks, offering a valuable tool for mitigating inference costs. Our reference implementation achieves up to 2times increase in inference throughput and even greater memory savings.

Autoregressive (AR) large language models (LLMs) have achieved remarkable performance across a wide range of natural language tasks, yet their inherent sequential decoding limits inference efficiency. In this work, we propose Fast-dLLM v2, a carefully designed block diffusion language model (dLLM) that efficiently adapts pretrained AR models into dLLMs for parallel text generation, requiring only approximately 1B tokens of fine-tuning. This represents a 500x reduction in training data compared to full-attention diffusion LLMs such as Dream (580B tokens), while preserving the original model's performance. Our approach introduces a novel training recipe that combines a block diffusion mechanism with a complementary attention mask, enabling blockwise bidirectional context modeling without sacrificing AR training objectives. To further accelerate decoding, we design a hierarchical caching mechanism: a block-level cache that stores historical context representations across blocks, and a sub-block cache that enables efficient parallel generation within partially decoded blocks. Coupled with our parallel decoding pipeline, Fast-dLLM v2 achieves up to 2.5x speedup over standard AR decoding without compromising generation quality. Extensive experiments across diverse benchmarks demonstrate that Fast-dLLM v2 matches or surpasses AR baselines in accuracy, while delivering state-of-the-art efficiency among dLLMs - marking a significant step toward the practical deployment of fast and accurate LLMs. Code and model will be publicly released.

Autoregressive language models, despite their impressive capabilities, struggle with complex reasoning and long-term planning tasks. We introduce discrete diffusion models as a novel solution to these challenges. Through the lens of subgoal imbalance, we demonstrate how diffusion models effectively learn difficult subgoals that elude autoregressive approaches. We propose Multi-granularity Diffusion Modeling (MDM), which prioritizes subgoals based on difficulty during learning. On complex tasks like Countdown, Sudoku, and Boolean Satisfiability Problems, MDM significantly outperforms autoregressive models without using search techniques. For instance, MDM achieves 91.5\% and 100\% accuracy on Countdown and Sudoku, respectively, compared to 45.8\% and 20.7\% for autoregressive models. Our work highlights the potential of diffusion-based approaches in advancing AI capabilities for sophisticated language understanding and problem-solving tasks.

Autoregressive models have demonstrated remarkable success in sequential data generation, particularly in NLP, but their extension to continuous-domain image generation presents significant challenges. Recent work, the masked autoregressive model (MAR), bypasses quantization by modeling per-token distributions in continuous spaces using a diffusion head but suffers from slow inference due to the high computational cost of the iterative denoising process. To address this, we propose the Fast AutoRegressive model (FAR), a novel framework that replaces MAR's diffusion head with a lightweight shortcut head, enabling efficient few-step sampling while preserving autoregressive principles. Additionally, FAR seamlessly integrates with causal Transformers, extending them from discrete to continuous token generation without requiring architectural modifications. Experiments demonstrate that FAR achieves 2.3times faster inference than MAR while maintaining competitive FID and IS scores. This work establishes the first efficient autoregressive paradigm for high-fidelity continuous-space image generation, bridging the critical gap between quality and scalability in visual autoregressive modeling.

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of "kick neurons" initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures - fully connected, cyclic, and linear-chain - reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

Masked diffusion models (MDM) are powerful generative models for discrete data that generate samples by progressively unmasking tokens in a sequence. Each token can take one of two states: masked or unmasked. We observe that token sequences often remain unchanged between consecutive sampling steps; consequently, the model repeatedly processes identical inputs, leading to redundant computation. To address this inefficiency, we propose the Partial masking scheme (Prime), which augments MDM by allowing tokens to take intermediate states interpolated between the masked and unmasked states. This design enables the model to make predictions based on partially observed token information, and facilitates a fine-grained denoising process. We derive a variational training objective and introduce a simple architectural design to accommodate intermediate-state inputs. Our method demonstrates superior performance across a diverse set of generative modeling tasks. On text data, it achieves a perplexity of 15.36 on OpenWebText, outperforming previous MDM (21.52), autoregressive models (17.54), and their hybrid variants (17.58), without relying on an autoregressive formulation. On image data, it attains competitive FID scores of 3.26 on CIFAR-10 and 6.98 on ImageNet-32, comparable to leading continuous generative models.

In this work, we propose Dimple, the first Discrete Diffusion Multimodal Large Language Model (DMLLM). We observe that training with a purely discrete diffusion approach leads to significant training instability, suboptimal performance, and severe length bias issues. To address these challenges, we design a novel training paradigm that combines an initial autoregressive phase with a subsequent diffusion phase. This approach yields the Dimple-7B model, trained on the same dataset and using a similar training pipeline as LLaVA-NEXT. Dimple-7B ultimately surpasses LLaVA-NEXT in performance by 3.9%, demonstrating that DMLLM can achieve performance comparable to that of autoregressive models. To improve inference efficiency, we propose a decoding strategy termed confident decoding, which dynamically adjusts the number of tokens generated at each step, significantly reducing the number of generation iterations. In autoregressive models, the number of forward iterations during generation equals the response length. With confident decoding, however, the number of iterations needed by Dimple is even only text{response length}{3}. We also re-implement the prefilling technique in autoregressive models and demonstrate that it does not significantly impact performance on most benchmark evaluations, while offering a speedup of 1.5x to 7x. Additionally, we explore Dimple's capability to precisely control its response using structure priors. These priors enable structured responses in a manner distinct from instruction-based or chain-of-thought prompting, and allow fine-grained control over response format and length, which is difficult to achieve in autoregressive models. Overall, this work validates the feasibility and advantages of DMLLM and enhances its inference efficiency and controllability. Code and models are available at https://github.com/yu-rp/Dimple.

We propose SDAR, a Synergistic Diffusion-Autoregression paradigm that unifies the training efficiency of autoregressive models with the parallel inference capability of diffusion. Instead of costly end-to-end diffusion training, SDAR performs a lightweight paradigm conversion that transforms a well-trained autoregressive (AR) model into a blockwise diffusion model through brief, data-efficient adaptation. During inference, SDAR generates sequences autoregressively across blocks for global coherence while decoding all tokens within each block in parallel via a discrete diffusion process. Extensive experiments show that AR models remain substantially more compute-efficient than masked diffusion models, providing a strong foundation for adaptation. Building on this insight, SDAR achieves efficient AR-to-diffusion conversion with minimal cost, preserving AR-level performance while enabling parallel generation. Scaling studies across dense and Mixture-of-Experts architectures confirm that SDAR scales without compromise: larger models exhibit stronger robustness to block size and decoding thresholds, yielding greater speedups without accuracy loss. Beyond efficiency, SDAR demonstrates enhanced reasoning and domain adaptability. Our 30B MoE model surpasses its AR counterpart on challenging scientific reasoning benchmarks such as GPQA and ChemBench, and gains further improvements under test-time scaling methods like majority voting and pass@k. Together, these results establish SDAR as a practical paradigm that combines the strengths of autoregression and diffusion for scalable, high-throughput reasoning.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

Recurrent fast-weight memories and selective state-space models compress an expanding context into a fixed-size recurrent state, making the state transition an online learning rule. We study this rule under read-after-write autoregressive semantics. For the prefix-prediction objective considered here, the local fast-memory example revealed at step t is the prefix-aligned pair (x_t,y_t)=(ϕ(k_{t-1}),v_t). The common same-step association (ϕ(k_t),v_t) remains causal, but optimizes a different internal objective. We derive normalized first-order updates for squared-error regression and negative inner-product objectives. The regression family comprises Falcon-1 (a scalar NLMS update), Falcon-2 (its per-column extension), and Falcon-3 (a sliding-window mini-batch update); Falcon-1A/Falcon-2A/Falcon-3A are the corresponding inner-product variants. We provide recurrent, masked-parallel, and chunk-parallel forms, together with numerically stable positive-decay renormalization. Representative variants remain competitive in language modeling and improve length extrapolation on variable-digit addition. This framework separates temporal alignment, plasticity, forgetting, and bounded rehearsal in recurrent sequence models.

Autoregressive large language models (LLMs) deliver strong performance but require inherently sequential decoding, leading to high inference latency and poor GPU utilization. Speculative decoding mitigates this bottleneck by using a fast draft model whose outputs are verified in parallel by the target LLM; however, existing methods still rely on autoregressive drafting, which remains sequential and limits practical speedups. Diffusion LLMs offer a promising alternative by enabling parallel generation, but current diffusion models typically underperform compared with autoregressive models. In this paper, we introduce DFlash, a speculative decoding framework that employs a lightweight block diffusion model for parallel drafting. By generating draft tokens in a single forward pass and conditioning the draft model on context features extracted from the target model, DFlash enables efficient drafting with high-quality outputs and higher acceptance rates. Experiments show that DFlash achieves over 6x lossless acceleration across a range of models and tasks, delivering up to 2.5x higher speedup than the state-of-the-art speculative decoding method EAGLE-3.

To compare autoregressive language models at scale, we propose using log-likelihood vectors computed on a predefined text set as model features. This approach has a solid theoretical basis: when treated as model coordinates, their squared Euclidean distance approximates the Kullback-Leibler divergence of text-generation probabilities. Our method is highly scalable, with computational cost growing linearly in both the number of models and text samples, and is easy to implement as the required features are derived from cross-entropy loss. Applying this method to over 1,000 language models, we constructed a "model map," providing a new perspective on large-scale model analysis.

Diffusion Language Models (DLMs) are rapidly emerging as a powerful and promising alternative to the dominant autoregressive (AR) paradigm. By generating tokens in parallel through an iterative denoising process, DLMs possess inherent advantages in reducing inference latency and capturing bidirectional context, thereby enabling fine-grained control over the generation process. While achieving a several-fold speed-up, recent advancements have allowed DLMs to show performance comparable to their autoregressive counterparts, making them a compelling choice for various natural language processing tasks. In this survey, we provide a holistic overview of the current DLM landscape. We trace its evolution and relationship with other paradigms, such as autoregressive and masked language models, and cover both foundational principles and state-of-the-art models. Our work offers an up-to-date, comprehensive taxonomy and an in-depth analysis of current techniques, from pre-training strategies to advanced post-training methods. Another contribution of this survey is a thorough review of DLM inference strategies and optimizations, including improvements in decoding parallelism, caching mechanisms, and generation quality. We also highlight the latest approaches to multimodal extensions of DLMs and delineate their applications across various practical scenarios. Furthermore, our discussion addresses the limitations and challenges of DLMs, including efficiency, long-sequence handling, and infrastructure requirements, while outlining future research directions to sustain progress in this rapidly evolving field. Project GitHub is available at https://github.com/VILA-Lab/Awesome-DLMs.

In this paper, we tackle the important yet under-investigated problem of making long-horizon prediction of event sequences. Existing state-of-the-art models do not perform well at this task due to their autoregressive structure. We propose HYPRO, a hybridly normalized probabilistic model that naturally fits this task: its first part is an autoregressive base model that learns to propose predictions; its second part is an energy function that learns to reweight the proposals such that more realistic predictions end up with higher probabilities. We also propose efficient training and inference algorithms for this model. Experiments on multiple real-world datasets demonstrate that our proposed HYPRO model can significantly outperform previous models at making long-horizon predictions of future events. We also conduct a range of ablation studies to investigate the effectiveness of each component of our proposed methods.