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Discrete Diffusion in Large Language and Multimodal Models: A Survey

Runpeng Yu, Qi Li, Xinchao Wang

arXiv:2506.13759v5cs.LGcs.AI

TL;DR

Autoregressive models limit parallel inference, structural control, and dynamic perception. This survey systematizes discrete diffusion language and multimodal models, their mathematical foundations, modeling, training, inference, quantization, trustworthy issues, and applications. The surveyed systems can achieve comparable performance to autoregressive counterparts while offering substantial speedups, including 10× decoding acceleration in reported industrial models.

  • Problem

    Autoregressive decoding hinders parallel inference, precise structural control, and dynamic perception.

  • Method

    The survey organizes discrete diffusion language and multimodal research across mathematical foundations, modeling, representative models, training, inference, quantization, trustworthy issues, and applications.

  • Results

    Reported discrete diffusion systems achieve comparable performance to autoregressive counterparts, with industrial models reporting 10× decoding speedups at about 1000 tokens per second.

  • Takeaways & Limitations

    Discrete diffusion is presented as a promising alternative to autoregressive language and multimodal modeling, with applications spanning language, vision-language, and biological domains.

Abstract

from arXiv · show

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 control, and dynamic perception. These capabilities are previously difficult to achieve with AR models. 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 10$\times$ acceleration in inference speed. These developments position discrete diffusion models as a promising alternative to intelligence based on the traditional autoregressive approach. 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, list commonly-used modeling methods, and categorize representative models. We further analyze key techniques for training, inference, quantization. We also discuss the trustworthy issues and summarize emerging applications across language, vision-language, and biological domains and etc.. We conclude by discussing future directions for research and deployment. Relative papers are collected in https://github.com/LiQiiiii/Awesome-Discrete-Diffusion-LLM_MLLM

I INTRODUCTION

Discrete diffusion models address autoregressive limitations by replacing left-to-right generation with parallel, controllable denoising. This survey organizes their foundations, models, methods, and applications while highlighting recent scalability and performance advances.

  • Autoregressive decoding limits parallel inference and precise control over output length and format.
  • Discrete diffusion generates multiple tokens per denoising step, accelerating inference relative to one-token-at-a-time decoding.
  • Predefined templates enable control over response length, format, and reasoning structure through denoising or infilling.
  • Bidirectional attention supports dynamic revision of visual and linguistic context throughout generation, unlike static one-pass perception.
  • 10× decoding speedups at about 1000 tokens per second accompany comparable code and mathematics performance for Mercury and Gemini Diffusion versus autoregressive counterparts.
  • The survey systematically covers mathematical foundations, modeling, representative models, training, inference, quantization, trustworthy issues, and applications.

III MODELING LANGUAGE DIFFUSION

The survey reviews modeling techniques that extend discrete diffusion beyond fixed-position, fixed-length denoising. These methods add blockwise conditioning, variable-length insertion, sub-token masking, or joint position and token refinement.

  • These modeling techniques aim to enhance controllability and flexibility in language diffusion.
  • III.A Block Diffusion Models: Block Diffusion models denoise sequence blocks while conditioning autoregressively on preceding blocks, interpolating between autoregressive and fully parallel generation.
  • III.B Flexible-Length Masked Diffusion: FlexMDM introduces an empty state so inference can insert new mask tokens and generate variable-length outputs.
  • Partial Masking decomposes tokens into sub-token sequences, adding an intermediate state beyond masked and ground-truth tokens.
  • III.D Diffusion with Optimal Transport Position Coupling: DDOT jointly denoises token values and positions, alternating token replacement with position refinement to support dynamic sequence restructuring.

IV REPRESENTATIVE MODELS

Representative models show discrete diffusion scaling from early formulations to large language, multimodal, and unified systems. The surveyed models combine bidirectional denoising with increasingly capable training and architectural strategies.

  • The model lineage spans early discrete diffusion foundations, scaled dLLMs, multimodal systems, and unified text-image models.
  • IV.C Unified Models: UniDisc treats images and captions as discrete token sequences and denoises both modalities jointly with a decoder-only Transformer using bidirectional attention.
  • IV.B Large Diffusion Language Models: DIFFUSION-LLMs scale discrete diffusion language models to 3B and 10B parameters, with performance improving consistently as model size increases.

reinforcement learning.

The surveyed models combine diffusion-based generation with varied training and inference strategies across language, multimodal, and unified settings. Representative systems target efficient scaling, controllable decoding, and competitive performance with autoregressive baselines.

  • Language models: DREAM 7B matches or exceeds similarly sized autoregressive models on many benchmarks through autoregressive initialization and context-adaptive noise scheduling.The recipe was developed through experiments at smaller scales before scaling to 7B parameters.
  • Language models: Seed Diffusion reaches 2,146 tokens per second on H20 GPUs while combining masked-language-modeling and edit-based noising.Its training loss combines mask prediction with overall reconstruction, and refined trajectory data supports sequential generation.
  • Multimodal models: Dimple uses two-stage hybrid training and confidence-based decoding, while autoregressive prefilling accelerates inference by about 1.5×–7× with minimal quality impact.Under the same training budget and dataset, Dimple-7B achieves higher aggregate multimodal benchmark scores than LLaVA-NEXT-7B.
  • Multimodal models: LaViDa improves multimodal alignment through complementary masking and accelerates inference by caching encoded image and prompt tokens with Prefix-DLM attention.It also applies timestep shifting to improve sample quality.
  • Unified multimodal models: Unified models extend discrete diffusion across modalities using shared architectures, multimodal reasoning, or discrete flow matching for self-correction.MMaDA uses a shared transformer and unified chain-of-thought format, while FUDOKI uses a metric-induced probability path and Muddit uses a multimodal diffusion transformer.

Diffusion-based GRPO

Diffusion-based preference optimization adapts reinforcement-learning objectives to discrete diffusion's structured, multi-step generation process. The surveyed methods target tractable objectives, lower variance, and better reward propagation across trajectories.

  • Diffusion-based GRPO: Diffusion-based GRPO methods incorporate structured noising, KL-regularized rewards, variance-reduced ELBO estimates, and per-step objectives for preference optimization.UniGRPO, VRPO, and SDPO respectively address structured policy optimization, intractable likelihoods, and reward propagation across trajectories.

Weighted Policy Optimization

Inference in discrete diffusion models combines token-scoring metrics with selection policies to decide which masked tokens to unmask, while remasking supports iterative refinement. These choices trade off decoding efficiency and performance.

  • Unmasking: Discrete diffusion models predict all response tokens each iteration but unmask only a selected subset, making token choice and count central inference decisions.The survey organizes these choices through random, metric-based, and policy-based unmasking strategies.
  • Metric-Based Unmasking: Metric-based unmasking assigns each token a score, including maximum probability, margin, negative entropy, and corpus-adjusted confidence.These metrics estimate prediction certainty or distribution peakedness and can downweight trivial high-frequency words.
  • Selection Policies: Selection policies determine how many scored tokens to unmask, including fixed top-st selection, confidence-threshold decoding, block-wise order, and dilated schedules.Confident Decoding adapts the number of parallel tokens to semantic difficulty, while block-wise decoding preserves a left-to-right order across blocks.
  • Remasking: Remasking reintroduces previously unmasked tokens so the model can revise low-confidence predictions during later denoising steps.General remasking controls the remasked-token ratio, while Wide-In Narrow-Out verifies decoded tokens with shadow tokens and replaces low-confidence ones with masks.
  • Prefilling and Caching: Prefilling and KV-cache techniques seek to avoid redundant computation, but their use in dLLMs and dMLLMs must account for iterative prediction of all response tokens.Unlike autoregressive decoding, only some masked tokens are unmasked at each iteration while the remainder stay masked.

classifier guidance

Guidance and trajectory-level inference methods steer discrete diffusion generation, while temporal voting, early stopping, context extension, and sparsity techniques target quality or efficiency. The survey also describes robustness beyond the training context length and adaptive response-length control.

  • Guidance: Guidance post-processes predicted logits or sampling probabilities to steer generation toward desired characteristics such as diversity or controllability.The survey distinguishes classifier-free, classifier-based, and reward-guided approaches.
  • Temporal Self-Consistency: Temporal self-consistency addresses temporal oscillation, where correct intermediate predictions can later be overwritten by incorrect outputs.It aggregates predictions across denoising steps with weighted voting and introduces Temporal Semantic Entropy for semantic uncertainty.
  • Particle Gibbs Sampling: Particle Gibbs sampling iteratively refines a reference trajectory using candidate particles, importance weighting, and resampling.The procedure begins with a single-particle trajectory and repeatedly updates it from reward-weighted candidates.
  • Early Stopping: Early stopping terminates decoding once confidence in a designated final-answer region is sufficient, rather than completing every denoising step.Predefined response templates or in-place prompts separate final-answer and reasoning regions.
  • Context Length and Efficiency: Bidirectional attention gives dLLMs observed robustness on extended contexts, including retrieval from recent input segments far beyond the training context length.LongLLaDA further extends context through NTK-aware RoPE scaling, while sparse block decoding reduces computation by filtering and gradually activating blocks.
  • Response Length Control: Response length can be controlled by dynamically inserting or deleting tokens, or by expanding sequences when EOS confidence or token confidence indicates insufficient length.These methods include special expand/delete tokens, insertion-count prediction, and threshold-based adaptive expansion.

VII QUANTIZATION

The survey connects discrete diffusion models to quantization, safety, and applications across language, multimodal, structured, and biological domains. It highlights distinct quantization challenges and middle-position safety vulnerabilities while documenting growing research activity.

  • VII QUANTIZATION: Post-training quantization studies report severe activation outliers in dLLMs, task-dependent sensitivity, and greater robustness in instruction-tuned than base models.These findings come from benchmarking mainstream quantization methods across multiple dLLM models.
  • VII QUANTIZATION: Conventional quantization degrades on dLLMs because errors accumulate across iterations and feature distributions vary across decoding steps, tokens, and channels.DLLMQuant addresses these issues with Temporal-Mask Adaptive Sampling, Interaction-Aware Activation Quantization, and Certainty-Guided Quantization.
  • VIII PRIVACY AND SAFETY: dLLMs introduce safety vulnerabilities associated with bidirectional context modeling and parallel decoding, which weaken defenses effective in autoregressive models.DIJA and PAD exploit interleaved mask-text prompts that preserve hazardous intent while forcing critical instructions into masked positions.
  • VIII PRIVACY AND SAFETY: dLLMs are more vulnerable to manipulation in the middle of responses than at initial tokens, motivating MOSA’s alignment of middle tokens with predefined safe tokens.The cited experiments report that middle-sequence alignment is more effective than alignment at the beginning.
  • Applications: Discrete diffusion applications span language reasoning, vision and motion synthesis, autonomous driving, graph prediction, and molecular or protein design.Examples include commonsense and knowledge-graph reasoning, unified vision-language-action decoding, scalable graph prediction, and molecular optimization.
  • Research Growth and Conclusion: The survey reports a consistent year-over-year increase in arXiv publications retrieved by keyword searches, reflecting growing research interest.Its conclusion presents dLLMs and dMLLMs as a comprehensive, evolving research area with applications and future directions.

- Appendix -

The appendix surveys discrete diffusion transition designs, reparameterized sampling, and divergence-based training objectives. It also records equivalences among score-matching and distribution-based losses, alongside practical limitations and inference optimizations.

  • Transition Matrices: Hybrid transitions combine absorbing and uniform processes to create more expressive discrete diffusion dynamics.Routlette Diffusion and GIDD study linear combinations of these transition types.
  • Reparameterized Discrete Diffusion: RDMs introduce Bernoulli routing variables that select token retention, noising, or denoising behavior during backward sampling.The reparameterized backward process uses a two-stage sampling procedure.
  • Reparameterized Discrete Diffusion: RDM inference cannot directly evaluate its routing indicator because the ground-truth sequence is unknown, so it recursively approximates the clean-token set.The recursion begins with b_T = 0, treating the initial sequence as fully noisy.
  • Training Losses: Concrete Score Matching uses squared-error ratio matching, but its ℓ2 loss may insufficiently penalize invalid predictions and cause instability.The stated problematic predictions include negative or zero values.
  • Training Losses: Target Concrete Score Matching offers score-based and distribution-based objectives, which are equivalent under the stated proposal distribution and divergence choices.The equivalence is stated for h(x1|x_t) = p1|t(x1|x_t), with corresponding divergence measures.
  • Inference Optimization: RADD caches network outputs when tokens remain unchanged, reducing the number of function evaluations during inference.This optimization follows from its reparameterized absorbing diffusion formulation.

APPENDIX B MODELING LANGUAGE DIFFUSION

The appendix describes language-diffusion variants that alter sequence structure, factor generation into blocks, or jointly denoise token values and positions. These designs extend discrete diffusion beyond fixed-length, fixed-position generation while retaining parallelism in selected dimensions.

  • Block Diffusion Models: Block Diffusion models partition sequences into blocks, denoise within each block, and condition autoregressively on preceding blocks.Inference is sequential across blocks but parallel within each block, with block-wise KV caching available.
  • Flexible-Length Masked Diffusion: FlexMDM assigns tokens empty, masked, or ground-truth states and alternates insertion with unmasking to generate variable-length outputs.Insertion expands the sequence with mask tokens, while unmasking predicts content for masked positions.
  • Position Coupling: DDOT jointly denoises token values and continuous token positions, enabling dynamic sequence restructuring while preserving relative ordering.Sampling alternates between token denoising and position refinement.

APPENDIX C TRAINING TECHNIQUES

The appendix surveys training techniques addressing efficient denoising, train–test input mismatch, reinforcement-learning alignment, and decoding-order control. The methods include teacher–student posterior matching, consistency objectives, stepwise preference optimization, and learned unmasking policies.

  • Distillation: Teacher–student distillation aligns student predictions with teacher posteriors at intermediate noise levels to transfer full-step generative knowledge.The reference distribution typically matches the forward diffusion at the chosen timestep.
  • Distillation: Consistency training requires agreement between multistep teacher–student denoising paths and direct student predictions across noise levels.The objective is expressed through a KL divergence and captures correlations without assuming independence.
  • Training–Inference Alignment: Training uses ground-truth noisy tokens while inference uses previously predicted tokens, creating an input discrepancy addressed by a two-step loss.The second loss compares the twice-denoised output with the ground-truth sequence.
  • Reinforcement Learning: SDPO decomposes trajectory-level preference alignment into per-step objectives because sampling and scoring entire denoising trajectories is computationally prohibitive.The resulting stepwise optimization is equivalent to a distribution-matching problem.
  • Reinforcement Learning: DCoLT trains a lightweight unmask policy to rank masked tokens and control the decoding order through top-K unmasking.Selected positions are then decoded by the standard diffusion language model.

APPENDIX D DECODING TECHNIQUES

The survey presents decoding techniques that refine discrete diffusion generation through remasking, classifier-based guidance, reward optimization, and energy-based sampling. These methods trade additional guidance or sampling computation for improved controllability, refinement, or output quality.

  • Unmasking and Remasking: Continuous-time remasking alternates between forward progression and stationary correction, respectively enabling iterative refinement or token adjustment within a fixed diffusion step.The distinction is controlled by the probability-flow condition: α_t−β_t=1 advances time, whereas α_t−β_t=0 reintroduces noise without time progression.
  • Classifier-Free Guidance: Classifier-free guidance combines conditional and unconditional predictions to adjust generation strength during diffusion sampling.The conditional prediction uses the prompt and noisy response, while the unconditional prediction uses mask tokens and the same response; w controls guidance strength.
  • Classifier-Free Guidance: Strong guidance during early decoding can severely degrade sample quality by accelerating unmasking and producing overly confident, premature token predictions.Column-wise normalization of the guided transition matrix is proposed to mitigate this degradation.
  • Classifier Guidance: Classifier guidance incorporates class-conditional preferences into blockwise sampling, enabling fine-grained attribute-conditioned generation under an intra-block independence approximation.The classifier signal modifies the model distribution, while γ controls its influence and candidate-token substitution reduces computational complexity.
  • Reward Guidance: Reward guidance uses an external reward model during inference to steer diffusion outputs without modifying the base model or applying guidance during training.TESS 2 converts model outputs into continuous representations, obtains scalar rewards, and performs gradient ascent with tunable coefficient η.
  • Energy-Based Diffusion: Energy-based diffusion reweights candidate denoising samples with an energy model, then uses importance sampling and backward-posterior updates to refine generation.The energy function may come from a pretrained AR model or a finetuned diffusion model, while local transition rates determine which tokens are updated.

APPENDIX E QUANTIZATION

The survey reviews DLLMQuant, which addresses quantization across iterative denoising by calibrating diverse timesteps, modeling attention-specific errors, and weighting tokens by certainty. Its components target errors that propagate across denoising steps and affect later predictions unevenly.

  • Overview: DLLMQuant combines Temporal-Mask Adaptive Sampling, Interaction-Aware Activation Quantization, and Certainty-Guided Quantization for dLLM quantization.The framework explicitly accounts for temporal masking, attention interactions, and token certainty.
  • Temporal-Mask Adaptive Sampling: Temporal-Mask Adaptive Sampling divides generation into blocks and selects calibration inputs across time intervals to cover diverse mask ratios.This addresses calibration variation across iterative generation steps.
  • Error Propagation: Quantization errors accumulate geometrically across denoising steps, making error propagation a central concern in dLLM quantization.The formulation tracks the quantization process, dequantization operation, and quantized model across timesteps.
  • Interaction-Aware Activation Quantization: Interaction-Aware Activation Quantization targets errors from multiplying softmax outputs with the attention value matrix by redefining the value-matrix quantization loss.The method uses the softmax output together with zero-point and scale-factor quantities.
  • Certainty-Guided Quantization: Certainty-Guided Quantization weights the Hessian by token certainty because masked, high-confidence tokens dominate subsequent denoising steps.The certainty-weighted Hessian prioritizes reducing quantization error on critical masked tokens.

APPENDIX F FUTURE DIRECTIONS

The survey identifies infrastructure, inference efficiency, scalability, security, and privacy as important deployment boundaries for dLLMs. It proposes standardized tooling and faster sampling while emphasizing unresolved risks from memorization, misuse, and holistic content generation.

  • Infrastructure: dLLM infrastructure remains relatively underdeveloped compared with autoregressive systems, motivating standardized modular frameworks and open pretrained models.The survey links this infrastructure gap to fairer comparisons, faster innovation, and practical deployment.
  • Inference Efficiency: dLLMs still face substantial limitations in inference efficiency and system scalability despite recent successes.Suggested directions include efficient attention, multi-scale token representations, progressive distillation, adaptive timestep scheduling, and INT8 or INT4 inference.
  • Security and Privacy: Diffusion models can memorize and reproduce sensitive training data, creating risks of privacy leakage and copyright violations.The survey also identifies harmful, false, or biased generation as a model-misuse and alignment concern.
  • Security and Privacy: Holistic dLLM generation makes real-time moderation non-trivial because problematic content may appear only after final denoising.The survey presents security, privacy, and alignment as issues requiring further work before responsible deployment at scale.
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