Diffusion Language Models

End-to-end autonomous driving via Vision-Language-Action (VLA) models demands a precarious balance between high-fidelity trajectory planning and efficient inference. Existing paradigms typically fall short: autoregressive (AR) VLAs are memory-bandwidth-bound on edge hardware and prone to exposure-bias drift, while full-sequence diffusion models preclude KV-cache reuse and suffer from "logical leakage" that violates the fundamental perceive-then-plan causality. We present Fast-dDrive, a block-diffusion VLA that performs bidirectional refinement within semantic units while enforcing strict causal ordering across them. Leveraging the observation that driving VLAs often emit structured JSON-like outputs, Fast-dDrive freezes structural tokens into a section scaffold and employs a section-aware training recipe that prioritizes safety-critical planning. We further introduce Scaffold Speculative Decoding to achieve AR-equivalent quality at significantly higher throughput. Finally, we propose a low-overhead test-time scaling scheme: by forking $N$ stochastic trajectory rollouts from a single shared-prefix KV cache and averaging them, we effectively suppress prediction variance at a fractional computational cost. Empirical results demonstrate that Fast-dDrive redefines the speed-accuracy frontier for driving agents. On the WOD-E2E test set, Fast-dDrive achieves SOTA ADE@3s and ADE@5s, alongside the highest RFS among diffusion-based VLAs; on nuScenes, it reduces average L2 error to $0.32$m (a $22\%$ improvement). When integrated with SGLang, our framework delivers $12\times$ throughput speedup over the AR baseline, narrowing the gap between high-capacity VLAs and the efficiency demands of real-time on-vehicle deployment.

When Masked Diffusion Models (MDMs) generate sequences through iterative refinement, the rich internal computation over masked positions is discarded, forcing every subsequent refinement step to recompute the valuable internal information stored as model representations. To avoid a hard reset between denoising rounds, we propose Learned Relay Representations (Relay), a method that allows MDMs to be forward-thinking when denoising by explicitly learning how to propagate latent information for the benefit of future denoising steps. Relay introduces a differentiable per-token channel that passes information between forward passes and is trained via truncated backpropagation through time (BPTT). We show that this framework can be scaled to state-of-the-art Diffusion Language Models (DLMs), and is seamlessly compatible with techniques like block diffusion and KV caching. We first provide a thorough justification of the design choices in Relay on a challenging Sudoku-based planning task. We then scale Relay to Fast-dLLM v2, a state-of-the-art DLM, outperforming standard supervised finetuning on coding tasks while reducing inference latency by up to 32%. Our empirical results demonstrate that state-of-the-art DLMs can be explicitly trained to relay latent information forward across decoding steps, advancing the performance-latency Pareto frontier. We provide code for all our experiments.

We aim to improve the reasoning capabilities of diffusion language models (DLMs). While SFT is a popular post-training recipe for autoregressive models, its use in DLMs faces challenges and can even hurt performance, though the underlying causes remain understudied. Our analysis reveals that vanilla SFT overlooks learnability, namely what and when tokens are learned. Specifically, rare tokens are difficult to learn when most of the input is masked, whereas it is straightforward and thus of little value to learn common tokens when most of the input is unmasked. Motivated by our analysis, we propose LIFT, an efficient SFT-based post-training algorithm for DLMs. LIFT learns easy tokens when most of the input is masked and hard tokens when more context is available, thus aligning the training with the information available at different diffusion time steps. Our results show that LIFT outperforms existing SFT baselines across six reasoning benchmarks, achieving up to a 3x relative gain on AIME'24 and AIME'25. Our code is publicly available at https://github.com/divelab/LIFT.

Discrete diffusion models are often trained through clean-data prediction, but the prediction can be used in different ways to define the reverse dynamics. In Masked Diffusion Models (MDM) these choices largely coincide, whereas in Uniform Diffusion Models (UDM) they do not. We show that the standard plug-in bridge parameterization for UDM is not optimized by the denoising posterior, but by a leave-one-out posterior that predicts each clean token without using its own noisy observation. This identifies a mismatch between the plug-in ELBO and the usual cross-entropy denoising objective. We characterize the leave-one-out target and derive exact conversions between the denoiser, the leave-one-out posterior, and the score. These conversions allow us to disentangle parameterization and training objective. Our results also lead to inference improvements without any additional training through an informed predictor-corrector sampler and improved temperature sampling based on the leave-one-out predictor. We further introduce an absorbing-state reformulation of uniform diffusion that preserves the UDM joint law while decomposing it into masked-diffusion-like sampling operations, with simpler denoising posteriors, carry-over unmasking, and a natural remasking mechanism. On language modeling, leave-one-out parameterizations consistently improve UDM generation, while the absorbing construction matches or surpasses masked diffusion. These results suggest that the empirical gap between masked and uniform diffusion is driven less by the choice of marginals themselves than by parameterization and sampling design. The code and models can be found at https://github.com/samsongourevitch/rev_udm.

Diffusion Language Models (DLMs) enable globally coherent, bidirectional, and controllable text generation, offering advantages over traditional autoregressive LLMs, while scaling to ultra-long sequences remains costly. Many existing block-sparse attention methods select blocks by fixed sampling patterns over the high-resolution attention space, such as tail regions or anti-diagonal stripes. Such prior-driven sampling can miss salient tokens and introduce instability under distribution shifts. In this paper, we propose the Block Approximate Sparse Attention framework (BA-Att) with block-wise pre-downsampled operation, which identifies informative regions within a compact downsampled space, avoiding reliance on brittle positional priors. To analyze its theoretical behavior, we define an oracle post-downsample attention map and formalize the approximation error between pre- and post-downsample schemes. Based on this insight, we introduce a lightweight norm-sorting module and a covariance-compensated correction that approximates full covariance using diagonal QK variances, reducing computational complexity. Extensive experiments show that our operator achieves up to 6.95x acceleration over FlashAttention in attention computation, and maintains near full-attention performance at 50% sparsity across language models, multimodal language models, and video generation models, demonstrating strong efficiency and generalization.

Discrete diffusion language models (DDLMs) generate text by iteratively denoising categorical token sequences, while recent drifting methods for continuous generators suggest that part of this sampling-time correction can instead be absorbed into training through an anti-symmetric fixed-point objective. We study how to transfer this principle to DDLMs, where the main challenge is the interface with discrete text: hard token samples are non-differentiable, and categorical predictions do not directly provide continuous samples to drift. We formulate TokenDrift, a drifting objective that lifts categorical predictions to soft-token features, applies anti-symmetric drifting in a frozen semantic space, and backpropagates the resulting stop-gradient feature target to DDLM logits. In controlled continual-training experiments with masked and uniform-state diffusion backbones, TokenDrift improves fixed-NFE generation quality over matched continuation baselines, reducing Gen.-PPL at 4 NFEs by 89% on MDLM and 86% on DUO. These results suggest that drifting can provide a practical refinement objective for DDLMs.

Masked diffusion language models (MDLMs) are emerging as a compelling new paradigm for text generation, but their training-time security remains largely unexplored. Existing backdoor attacks on Gaussian diffusion models or autoregressive language models do not directly apply to MDLMs because MDLMs rely on discrete state corruption and iterative denoising rather than continuous noising or left-to-right prediction. In this work, we present the first systematic study of training-time backdoor attacks on MDLMs. We propose SHADOWMASK, a backdoor attack that modifies the MDLM forward corruption process by replacing the standard all-mask terminal distribution with a trigger-mask mixture prior. This creates a dedicated denoising pathway from trigger-corrupted states to attacker-specified targets while preserving clean denoising behavior. We further provide a principled mathematical formulation by defining the backdoored forward process, deriving the reverse-time posterior, and obtaining the continuous-time training objective. Evaluations on DiT-based MDLM and LLaDA-8B-Instruct across WikiText-103, OpenWebText, and Alpaca show that SHADOWMASK achieves near-100% attack success, substantially outperforms standard data poisoning, largely preserves clean utility, remains effective under full-model and parameter-efficient fine-tuning, and is robust against representative defenses.

While diffusion has drawn considerable recent attention from the language modeling community, continuous diffusion has appeared less scalable than discrete approaches. To challenge this belief we revisit Plaid, a likelihood-based continuous diffusion language model (DLM), and construct RePlaid by aligning the architecture of Plaid with modern discrete DLMs. In this unified setting, we establish the first scaling law for continuous DLMs that rivals discrete DLMs: RePlaid exhibits a compute gap of only $20\times$ compared to autoregressive models, outperforms Duo while using fewer parameters, and outperforms MDLM in the over-trained regime. We benchmark RePlaid against recent continuous DLMs: on OpenWebText, RePlaid achieves a new state-of-the-art PPL bound of $22.1$ among continuous DLMs and superior generation quality. These results suggest that continuous diffusion, when trained via likelihood, is a highly competitive and scalable alternative to discrete DLMs. Moreover, we offer theoretical insights to understand the advantage of likelihood-based training. We show that optimizing the noise schedule to minimize the ELBO's variance naturally yields linear cross-entropy (information loss) over time. This evenly distributes denoising difficulty without any case-specific time reparameterization. In addition, we find that optimizing embeddings via likelihood creates structured geometries and drives the most significant likelihood gain.

Recent masked diffusion language models (MDLMs), such as LLaDA and Dream, have achieved performance comparable to autoregressive large language models. Unlike autoregressive models, which generate text sequentially, MDLMs generate text by iteratively denoising masked positions in parallel. During fine-tuning, MDLMs learn to recover responses from masked response states conditioned on a prompt, thereby shifting their predictions from a prompt-masked unconditional distribution toward a prompt-conditional distribution. Despite this distinct generative and fine-tuning mechanism, machine unlearning for MDLMs remains largely unexplored. In this paper, we propose Masked Diffusion Unlearning (MDU), the first unlearning framework for MDLMs, by revisiting the process of learning specific knowledge in terms of diffusion. Specifically, MDU minimizes a forward KL divergence from the prompt-conditional prediction to a prompt-masked unconditional anchor at every masked response position, with a temperature scaling parameter to control the privacy-utility trade-off. Our empirical results on standard benchmarks and MDLM backbones show that MDU achieves high unlearning performance compared to existing LLM unlearning methods. Code is available at https://github.com/leegeoru/MDU.

Unlike autoregressive models, which generate one token at a time, dLLMs denoise a chunk of [MASK] tokens jointly and sample one or more tokens per step; despite enabling parallel decoding, this process incurs substantial computational cost due to the large chunk size of masked tokens. We observe that much of this cost is spent on repeatedly processing the preceding context and many [MASK] tokens with the same feature representations, indicating considerable computational redundancy. In this work, we revisit dLLM's redundancy from the perspective of [MASK] tokens. Through systematic analysis, we verify the redundancy of [MASK] tokens while revealing their critical role in providing structural information. Guided by these findings, we propose position-preserving [MASK] token compression and terminal-aware augmentation. By compressing redundant [MASK] computation, this approach accelerates decoding and further provides a natural extension toward context-folding-like long-context scaling under limited input-length constraints for full-sequence dLLMs such as LLaDA-8B-Instruct and LLaDA-1.5. Moreover, for block dLLMs such as LLaDA2.0-mini, it augments the context with a protected terminal [MASK] token to enhance generation quality with negligible overhead.

Prompt compression reduces inference cost and context length in large language models, but prior evaluations focus mainly on autoregressive architectures. This study examines whether LLMLingua-2 transfers effectively to diffusion large language models (DLLMs), specifically LLaDA-8B-Instruct. We evaluate GSM8K, DUC2004, and ShareGPT using 250 prompts per dataset at an approximate 50% compression ratio, covering mathematical reasoning, prompt reconstruction, and summarization. Outputs from original, compressed, and reconstructed prompts are compared using exact-match accuracy, BLEU, ROUGE, and BERTScore. Results show that high semantic preservation does not necessarily ensure stable downstream behavior in diffusion models. Summarization remains relatively robust, while mathematical reasoning degrades substantially despite high semantic similarity. Reconstruction further shows that semantically similar prompts may omit reasoning-critical information needed for stable denoising. Overall, compression failures are mainly driven by information omission rather than semantic drift, suggesting that autoregressive prompt compression methods may not transfer uniformly to DLLMs. These findings motivate diffusion-aware compression strategies.

Radiology report generation (RRG) aims to automatically produce clinically accurate textual reports from medical images. Existing methods predominantly rely on autoregressive (AR) language models, whose causal dependency structure restricts generation to a unidirectional left-to-right process. This paradigm can induce sequence bias, where models tend to follow stereotypical token orders and high-frequency report templates rather than fully grounding generation in image-specific evidence. In this paper, we propose AnchorDiff, the first masked-diffusion framework for RRG that integrates knowledge-graph-derived clinical anchors into diffusion language modeling. By leveraging bidirectional context and iterative refinement, AnchorDiff mitigates the limitations of fixed-order autoregressive decoding. Specifically, we introduce a topology-aware training strategy that uses RadGraph-derived entity hierarchies to assign clinically important tokens differentiated masking protection and loss weights. We further design an inference-time rewriting strategy that detects unstable committed tokens through perturbation-based testing and selectively revises them during denoising. Extensive experiments on the MIMIC-CXR and MIMIC-RG4 benchmarks demonstrate that AnchorDiff achieves state-of-the-art (SOTA) performance, showing the effectiveness of clinically anchored masked diffusion for radiology report generation.

Diffusion Large Language Models (DLLMs) promise fast parallel generation, yet open-source DLLMs still face a severe quality-speed trade-off: accelerating decoding by revealing multiple tokens often causes substantial quality degradation. We attribute this dilemma to a train-inference mismatch amplified by irreversible decoding. While training reconstructs tokens from randomly corrupted states, efficient inference requires an adaptive denoising order, where easier tokens are revealed earlier and context-dependent ones are deferred. This view motivates two complementary methods: an inference-time method that makes parallel decoding revokable, and a training-time extension that distills the reliable order exposed by this revokable process. Accordingly, we first propose Wide-In, Narrow-Out (WINO), a training-free decoding algorithm that enables revokable parallel generation. WINO aggressively drafts multiple tokens, verifies generated tokens with enriched global context, and re-masks unreliable ones for later refinement. Building on this discovered order, we further introduce WINO+, which injects the verified denoising trajectories produced by WINO into model parameters, aligning training with efficient inference. Experiments on LLaDA and MMaDA show that WINO improves both quality and efficiency, while WINO+ further strengthens this progression. On GSM8K, WINO improves accuracy from 73.24% to 75.82% with a 6.10x step reduction, and WINO+ further achieves 76.58% with a 6.83x reduction. On Flickr30K, WINO+ reaches a 16.22x step reduction with improved CIDEr. These results demonstrate that DLLMs can serve as their own efficiency teachers by first discovering reliable denoising orders through revokable decoding and then learning to follow them for faster generation. Code is available at https://github.com/Feng-Hong/WINO-DLLM/tree/WINO-plus.

Block discrete diffusion language models factorize a sequence autoregressively over fixed-size positional blocks, decoupling within-block parallel denoising from across-block conditioning. We argue that this rigid partition wastes structure already present in the sequence: blocks defined by position rather than by content separate semantically coherent tokens and group unrelated ones together. We introduce the Dynamic Chunking Diffusion Model (DCDM), which replaces positional blocks with content-defined semantic chunks. At its core is Chunking Attention, a differentiable layer that routes tokens into $K$ clusters parameterized by learnable subspaces and shaped end-to-end by the diffusion objective. The resulting cluster assignments induce a chunk-causal attention mask under which a discrete diffusion denoiser factorizes the sequence likelihood autoregressively over semantic chunks, strictly generalizing block discrete diffusion. On downstream benchmarks at parameter scales up to 1.5B, DCDM consistently improves over both unstructured and positional-block diffusion baselines, with the advantage stable across scales and visible early in training.

Proteins perform their biological functions through three-dimensional structures encoded by amino acid sequences, and ligand-binding protein co-design requires models that generate sequence-structure compatible proteins under explicit ligand constraints. Although continuous diffusion and flow-based models support ligand-aware design in coordinate or latent spaces, existing discrete diffusion protein language models mainly operate over sequence or structure tokens without direct small-molecule conditioning. We introduce \textbf{ProtLiD$^2$}, a Protein Ligand-conditioned Discrete Diffusion model for protein sequence-structure co-design. ProtLiD$^2$ jointly generates amino-acid sequence and discrete structure tokens while incorporating ligand chemical and geometric information through geometry-aware cross-attention. Trained on over one million ligand-protein complexes, ProtLiD$^2$ extends masked discrete diffusion to ligand-aware functional protein design. We further propose maximum confidence-margin guided ReMask decoding, an inference-time self-correction strategy that retains confident predictions and remasks uncertain tokens. ProtLiD$^2$ improves global fold confidence over Complexa in whole-protein design, increasing TM-score from 0.672 to 0.802 and pLDDT from 64.55 to 73.00. In pocket co-design, ProtLiD$^2$ reduces active-site BB-RMSD from 3.46/3.40Å for FAIR/PocketGen to 1.97Å, and improves ligand-aware pass rates over PocketGen from 14.86% to 59.73% and from 6.08% to 23.49% under stricter docking thresholds. These results support ligand-conditioned discrete diffusion as an effective token-space framework for functional protein co-design. Code will be available at https://github.com/auroua/ProtLiD.

Diffusion large language models (dLLMs) generate text by iteratively denoising masked token sequences. Although dLLMs can predict all masked positions in parallel within each step, the large number of denoising iterations still makes inference expensive. This cost can be reduced spatially by unmasking multiple tokens per step, or temporally by collapsing multiple denoising steps into one verification call. We propose Parallel Speculative Decoding (PSD), a training-free framework that jointly improves inference along both axes. Using the confidence scores from a single forward pass, PSD selects positions to unmask via a configurable, adaptive unmasking policy and constructs multi-depth speculative drafts without extra model calls. A final batched verification pass then applies hierarchical acceptance, keeping the deepest draft that remains consistent with the updated predictions. Experiments on three dLLMs across reasoning and code generation tasks show that PSD achieves favorable trade-offs between inference efficiency and generation quality, reaching up to $5.5\times$ tokens per forward pass with accuracy comparable to greedy decoding.

Continuous diffusion and flow models are attractive for non-autoregressive text generation because they can update all positions in parallel. A major difficulty is the interface between continuous latent states and discrete tokens. This report studies a draft-conditioned latent refinement model built from a frozen BERT encoder, a parallel decoder, a denoising DraftPrior, a local FlowNet, and a learned diagonal MetricNet. Early Gaussian-start experiments showed that good latent-space metrics, such as scale matching or cosine similarity, do not guarantee good decoding. Generated latents can be close to real encoder latents but still produce high-entropy, biased, or repetitive token distributions. We therefore frame the task as controlled local refinement rather than full generation from noise. On ROCStories, using the first two sentences as prompt and the last three as target, full 768-dimensional BERT latents recover tokens much better than compressed 256-dimensional latents. With 768-dimensional latents, DraftPrior target-token probability is 0.938 for clean drafts, 0.613 for 3% token dropout, 0.483 for 5% dropout, and 0.272 for 10% dropout. Local flow refinement and fused decoder-aware readout give modest additional gains, while metric learning and OT-style alignment improve geometry but do not close the decoder gap. The main result is a diagnostic one: latent geometry alone is not enough. Continuous latent text generation should be evaluated by decoder recoverability, the quality of the start distribution, and whether refinement preserves decoder-readable structure.

Masked Diffusion Language Models MDLMs replace autoregressive generation with iterative demasking and their privacy properties are largely unstudied. We study membership inference attacks MIA on fine tuned MDLMs and show they are significantly more vulnerable than current grey box baselines suggest. We extract a 46 dimensional feature vector from the models reconstruction loss at four masking ratios and train XGBoost and MLP classifiers on top. On the MIMIR benchmark across six text domains XGBoost achieves mean AUC 0.878 peaking at 0.930 on Pile CC and beats the SAMA grey box baseline by 0.062 AUC on average. A leave one signal out ablation shows that the ELBO trajectory alone drives most of this with a mean drop of 0.130 when removed while attention features add almost nothing below 0.003. We also design a shadow model transfer attack where K equals 3 surrogate MDLMs trained on data from unrelated domains generate classifier labels with no access to the target domain. This achieves 0.858 mean AUC within 0.020 of the white box oracle and establishes shadow model transfer as a practical and near equally effective attack path.

Large Language Diffusion Models (LLDMs) are emerging as an alternative to autoregressive models, offering faster inference through higher parallelism. Similar to autoregressive LLMs, they remain prone to hallucinations, making reliable uncertainty quantification (UQ) crucial for safe deployment. However, existing UQ methods are fundamentally misaligned with this new paradigm: they assume autoregressive factorization or use expensive repeated sampling, negating the efficiency of LLDMs. In this work, we present the first systematic study of UQ for LLDMs and propose lightweight, zero-shot uncertainty signals derived from the iterative denoising process, leveraging intermediate generations, token remasking dynamics, and denoising complexity. We further adapt a state-of-the-art UQ method to LLDMs by combining masked diffusion likelihoods with trajectory-based semantic dissimilarity. We prove that expected trajectory dissimilarity lower bounds the masked diffusion training objective, which motivates its usage as an uncertainty score. Comprehensive experiments across three tasks, eight datasets, and two models show that our method achieves a great cost-performance trade-off: it approaches the strongest sampling-based baselines while incurring up to 100x lower computational overhead. Our work demonstrates that LLDMs can deliver both fast inference and reliable hallucination detection simultaneously.

This work reformulates language generation as a stochastic optimal control problem, providing a unified theoretical perspective to analyze autoregressive and diffusion models and explain their limitations (Efficiency-Fidelity Paradox, Irreversibility Error Propagation, Optimization Tractability and Fidelity) in terms of combination of trajectory singularity, adjoint state vanishing, and gradient absence. To address these issues, we approximate the solution to the Hamilton-Jacobi-Bellman (HJB) equation, yielding an optimal policy that acts as a closed-loop controller. To bypass the intractability of directly solving the HJB PDE, we employ Flow Matching as the optimal trajectory solver within the rectified latent control space. This allows our Manta-LM with Global Integral Operator to approximate the global vector field, effectively realizing a model that simultaneously achieves high-fidelity text generation and efficient, low-cost parallel sampling. Empirically, our method achieves strong performance on language modeling and conditional generation tasks, while exhibiting improved stability, efficiency, and controllability.

Multi-step LLM reasoning over structured tables fails because planning and execution share no explicit cell-grounding contract. Existing methods constrain the planner to a left-to-right factorization at odds with table permutation invariance, and score intermediate states by generated content alone, overlooking cell grounding. We conduct a pilot study showing that diffusion language models (DLMs) produce more human-aligned and permutation-stable cell attention on tables than autoregressive models, with a 40.2% median reduction in attention-AUROC variability under row reordering. Motivated by this, we propose TABALIGN, a planned table reasoning framework that operationalizes the contract. TABALIGN pairs a masked DLM planner, whose bidirectional denoising emits plan steps as binary cell masks, with TABATTN, a lightweight verifier trained on 1,600 human-verified attention standards to score each step by its attention overlap with the plan-designated mask. Across eight benchmarks covering table question answering and fact verification, TABALIGN improves average accuracy by 15.76 percentage points over the strongest open-source baseline at comparable 8B-class scale, with a matched-backbone ablation attributing 2.87 percentage points of this gain to the DLM planner over an AR planner on a fixed reasoner. Cleaner DLM plans also accelerate downstream reasoning execution by 44.64%.

Continuous diffusion language models require choosing a representation space in which denoising operates, yet it remains unclear which representations are most compatible with diffusion. We study a basic design question: where inside a pretrained language model should continuous diffusion operate? We formulate this as a hidden-state interface-selection problem and hypothesize that diffusion-friendly interfaces can be identified from representation geometry. We operationalize this hypothesis using three training-free geometric proxies: local compactness, global stiffness, and effective rank. Across two 8B-scale backbones, the resulting geometry score predicts fixed-budget diffusion bridgeability beyond the dominant effect of layer depth. We then instantiate DiHAL, a Locate-and-Replace framework that replaces the transformer prefix below a selected interface with conditional diffusion while retaining the pretrained suffix and LM head. Under full training, geometry-selected interfaces remain close to validation-loss oracles and outperform worst-layer controls, while the diffusion bridge outperforms a parameter-matched deterministic replacement under matched diagnostic conditions. These results suggest that the representation space in which diffusion operates should itself be treated as a first-class design variable for continuous diffusion in language models.

Discrete diffusion language models improve generation efficiency through parallel token prediction, but standard $X_0$ prediction methods introduce factorization errors by approximating the clean token posterior with independent token-wise distributions. This paper proposes Factorization-Error-Free Discrete Diffusion Language Modeling (FeF-DLLM), which replaces independent clean-token prediction with an exact prefix-conditioned factorization of the clean posterior to better preserve token dependencies. To reduce the sequential cost introduced by prefix conditioning, FeF-DLLM further incorporates speculative decoding within diffusion denoising, accelerating inference while maintaining the parallel prediction and re-masking properties of DLLMs. Theoretically, we prove that FeF-DLLM generates from the true joint distribution and derive its expected acceleration ratio. Experiments on GSM8K, MATH, HumanEval, and MBPP demonstrate that our method improves accuracy by an average of 5.04 percentage points while achieving an average inference speedup of $3.86\times$.

Discrete diffusion models are increasingly competitive for language modeling, yet it remains unclear how their denoising objectives organize learning. Although these objectives target the full data distribution, we show that the exact reverse process induces a hierarchy between coarse support information and finer frequency information. For uniform and absorbing (a.k.a. masking) diffusion, we prove that, in the small-noise regime of the final denoising steps, each single-token reverse edit decomposes into a leading scale, determined by whether it moves toward the data support (e.g., grammatically valid sentences), and a finer coefficient, determining relative probabilities within the same scale. Thus, recovering validity structure only requires learning the correct order of magnitude of reverse probabilities, whereas recovering data frequencies requires coefficient-level estimation. The separation is mechanism-dependent: uniform diffusion exhibits a trichotomy into validity-improving, validity-preserving, and validity-worsening edits, while absorbing diffusion places its leading-order mass on validity-improving moves. Experiments on a masked language diffusion model and synthetic regular-language tasks support these predictions: support-localization emerges earlier than within-support frequency ranking, and the contrast between uniform and absorbing diffusion matches the predicted rate separation. Together, our results suggest that discrete diffusion models learn data support before data frequencies.

Diffusion language models are a promising alternative to autoregressive models, yet post-training methods for them largely adapt reward-maximizing objectives. We identify a central failure mode in this setting we call trajectory locking: sampled reward-driven updates over-concentrate probability mass onto a narrow set of denoising paths, reducing coverage of alternative correct solutions under repeated sampling. To address this, we propose TraFL (Trajectory Flow baLancing), a trajectory-balance objective that trains the policy toward a reward-tilted target distribution anchored to a frozen reference model. We make this practical for diffusion language models with a diffusion-compatible sequence-level surrogate and a learned prompt-dependent normalization. Across mathematical reasoning and code generation benchmarks, TraFL is the only evaluated post-training method that improves over the base model in every benchmark-length setting, with gains that persist as the sampling budget increases. The improvements transfer to held-out evaluations: TraFL stays above the base model on Minerva Math and is the strongest method on every LiveCodeBench difficulty split.

While autoregressive (AR) Vision-Language-Action (VLA) models have demonstrated formidable reasoning capabilities in robotic tasks, their sequential decoding process often incurs high inference latency and may amplify error accumulation during long-horizon execution. Discrete Diffusion Language Models (dLLMs) provide a promising alternative through parallel token refinement, but their practical deployment in robotics remains limited by repeated denoising function evaluations (NFEs) and the difficulty of directly applying standard KV caching to bidirectional iterative decoding. To bridge these paradigms, we propose BlockVLA, a framework that adapts pretrained AR backbones into an efficient discrete diffusion policy through a block diffusion paradigm. BlockVLA maintains autoregressive dependencies at the block level while enabling parallel denoising within each block, thereby combining global causal coherence with local parallel generation. This design enables prefix KV-cache reuse across completed blocks, reduces the effective cost of iterative denoising, and provides a smoother transition from AR pretraining to diffusion-based policy fine-tuning. We conduct extensive evaluations on the LIBERO and SimplerEnv benchmarks. Experimental results demonstrate that our BlockVLA achieves a 3.3$\times$ inference acceleration over standard discrete diffusion baselines. Furthermore, our model exhibits superior training efficiency, with success rates converging substantially faster than baselines, a gain that is particularly pronounced in complex, long-horizon tasks, where BlockVLA achieves significant performance gains in the early stages of training. This work establishes Block Diffusion as a robust bridge between large-scale pretrained AR models and efficient, high-frequency real-time robotic control.

Diffusion Language Models(DLMs) provide a promising alternative to autoregressive language models through iterative denoising and bidirectional generation. However, their iterative generation process introduces distinct safety vulnerabilities because harmful content can emerge at arbitrary positions and persist across subsequent denoising steps. Existing defenses rely on fixed interventions or aggressive remasking, which limits adaptive control over denoising trajectories and can degrade generation quality. We propose an inference-time defense framework that combines adaptive safety steering with safety-aware remasking. Our method uses a gating direction to continuously adjust steering strength from the current denoising state and applies a steering direction to masked positions to guide subsequent predictions toward safer trajectories. Our method further employs a lightweight response detector after the first generation block to identify unsafe trajectories at an early stage. The detector triggers targeted remasking over generated content and part of the conditioning prompt, and the model regenerates the selected positions under adaptive safety steering. This design combines continuous trajectory control with explicit correction of unsafe content while requiring no modification of model parameters. Experiments on LLaDA and Dream demonstrate that our method improves robustness against diverse jailbreak attacks while preserving benign generation quality and general model capability. Our code is available at https://anonymous.4open.science/r/DLM_Steering-C32B/.

Masked diffusion models (MDMs) have emerged as a promising alternative to autoregressive models (ARMs) for language modeling. However, MDMs are known to learn substantially more slowly than ARMs, which may become problematic when scaling MDMs to larger models. Therefore, we ask the following question: how can we accelerate standard MDM training while maintaining its final performance? To this end, we first provide a detailed analysis of why MDM training is slow. We find that the main factor is the locality bias of language: the predictive information for a token is concentrated in nearby positions. We further investigate how this bias slows learning and suggest a simple yet effective remedy: bell-shaped time sampling as a training strategy. Notably, MDMs trained with our training recipe reach the same validation negative log-likelihood (NLL) up to $\sim4\times$ faster than standard training on One Billion Word Benchmark (LM1B). We also show faster improvements in generative perplexity, zero-shot perplexity, and downstream task performance on various benchmarks.

Modern language models have historically relied on two dominant design choices: subword tokenization and autoregressive (AR) ordering. These design decisions bake in priors that dictate a model's learning. Recently, two alternative paradigms have challenged this: byte-level modeling, which bypasses static statistically-derived token vocabularies, and masked diffusion modeling (MDM), which conducts parallel, non-sequential generation. Their intersection represents a fully end-to-end modality-agnostic generative prototype; however, removing these structural priors incurs a significant computational cost. In this work, we investigate this cost through a compute-matched scaling study. Our results reveal that the performance penalty of byte modeling is not uniform; across scale, the scaling overhead of byte modeling is worse for MDM than for AR. We hypothesize that this disparity stems from context fragility: while AR's stable causal history allows models to naturally rediscover subword patterns, the MDM objective destroys the local contiguity required to efficiently resolve semantics from raw bytes. Our findings from controlled permutation experiments suggest that future modality-agnostic designs must incorporate alternative structural biases to maintain viable scaling trajectories in the byte regime.

Continuous diffusion is a natural framework for non-autoregressive generation but has generally lagged behind masked discrete diffusion models (MDMs) on discrete sequence generation. We argue that the bottleneck is not continuity itself, but a representation in which denoising depends on timestep-indexed noise regimes. We introduce Discrete Stochastic Localization (DSL), a continuous-state framework with unit-sphere token embeddings whose Bayes-optimal denoiser is invariant to the nominal signal-to-noise ratio (SNR) under the localization channel. One trained network then supports an entire family of per-token SNR paths, with endpoint masked-diffusion paths as a special case. Fine-tuning a pretrained MDLM checkpoint with DSL substantially improves distributional faithfulness (MAUVE) on OpenWebText across all step budgets from $T{=}128$ to $T{=}1024$, and the same checkpoint supports random-order autoregressive sampling, as well as a hybrid continuous-then-discrete sampler using as few as T=48 total steps -- without distillation or retraining.