Diffusion Language Models

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 \textbf{D}ynamic \textbf{C}hunking \textbf{D}iffusion \textbf{M}odel (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 \textbf{Prot}ein \textbf{L}igand-conditioned \textbf{D}iscrete \textbf{D}iffusion 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.

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.

Continuous diffusion language models lag behind autoregressive transformers, partly because diffusion is applied in spaces poorly suited to language denoising and token recovery. We propose DiHAL, a geometry-guided diffusion-transformer hybrid that asks where diffusion should enter a pretrained transformer. DiHAL scores layers with geometry-based proxies, selects a diffusion-friendly hidden-state interface, and replaces the lower transformer prefix with a diffusion bridge while retaining the upper layers and original LM head. By reconstructing the selected-layer hidden state rather than tokens, DiHAL avoids direct continuous-to-discrete recovery. Experiments on 8B-scale backbones show that the geometry score predicts effective shallow insertion layers under a fixed bridge-training protocol and that hidden-state recovery improves over continuous diffusion baselines in a diagnostic comparison matching the diffusion/recovery training budget. These results suggest that hidden-state geometry helps identify where diffusion-based replacement is feasible inside pretrained 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.

Flow Language Models (FLMs) are a recently introduced class of language models which adapt continuous flow matching for one-hot encoded token sequences. Their denoisers have a special structure absent from generic continuous diffusion models: each block of the denoising mean is a posterior marginal distribution over the clean token at that position. Standard DDPM-style samplers collapse these marginals to a single conditional-mean endpoint and bridge toward this simplex-valued point, which is generally not a valid one-hot sequence. We argue that the natural sampler for an FLM is instead posterior-predictive. At each reverse step, we sample a clean one-hot endpoint from the factorized posterior defined by the FLM token marginals, and then sample the next continuous state from the analytic Ornstein--Uhlenbeck bridge conditioned on that endpoint. The method is training-free, uses the same model evaluations as standard sampling, and gives a principled interface for token-level decoding controls such as temperature scaling and nucleus truncation. We show that, under exact posterior marginals, the endpoint approximation error is exactly the conditional multi-information among token positions. The induced one-step bridge kernel preserves all token-wise posterior-predictive marginals and loses only the residual cross-position dependence. Finally, we prove a Girsanov path-space comparison showing that the marginal-conditioned bridge has a no-larger denoising-error term than the frozen conditional-mean bridge, with strict improvement whenever intermediate coordinate-wise bridge observations reveal additional information about the clean token. Experiments with FLMs show that the sampler improves the quality--diversity tradeoff. Code is available at: github.com/imbirik/mcb.

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 by generating text through iterative denoising and bidirectional refinement. However, this iterative generation paradigm also introduces unique safety vulnerabilities when harmful tokens generated at intermediate denoising steps propagate through subsequent refinement processes and eventually induce unsafe outputs. While there are a few attempts to remedy this issue, they either fail to generate safe outputs or generate safe yet low-quality outputs. This motivates us to propose an inference-time defense framework based on the step-wise intervention during the denoising process, which then improves the safety without compromising the output quality. The key component of our framework is a contrastive safety direction (SGD), a latent direction that captures the semantic boundary between harmful and safe generations. We leverage SGD to assess the alignment of generated tokens with harmful semantics at each denoising step. When harmful alignment is detected, our method remasks the corresponding tokens and resumes the denoising process with adaptive steering, where the steering strength is modulated according to the estimated degree of harmfulness. As a plug-and-play module, our method circumvents the need for additional fine-tuning and can be directly incorporated into off-the-shelf diffusion models. The experimental results show that our approaches reduce jailbreak success rates to 0.64% while preserving generation quality close to the original model performance. This confirms the effectiveness of step-wise intervention for safe diffusion language model generation. Our code is available at https://github.com/leeyejin1231/DLM_Steering_Remasking.

We introduce Orthrus, a simple and efficient dual-architecture framework that unifies the exact generation fidelity of autoregressive Large Language Models (LLMs) with the high-speed parallel token generation of diffusion models. The sequential nature of standard autoregressive decoding represents a fundamental bottleneck for high-throughput inference. While diffusion language models attempt to break this barrier via parallel generation, they suffer from significant performance degradation, high training costs, and a lack of rigorous convergence guarantees. Orthrus resolves this dichotomy natively. Designed to seamlessly integrate into existing Transformers, the framework augments a frozen LLM with a lightweight, trainable module to create a parallel diffusion view alongside the standard autoregressive view. In this unified system, both views attend to the exact same high-fidelity Key-Value (KV) cache; the autoregressive head executes context pre-filling to construct accurate KV representations, while the diffusion head executes parallel generation. By employing an exact consensus mechanism between the two views, Orthrus guarantees lossless inference, delivering up to a 7.8x speedup with only an O(1) memory cache overhead and minimal parameter additions.

Diffusion Language Models (DLMs) generate text by iteratively denoising masked token sequences, offering a tradeoff between parallelism and quality compared to autoregressive models. In current practice, the number of tokens decoded per step is controlled by a confidence threshold, and quality degrades monotonically as more tokens are denoised per step. We introduce Multi-token Residual Prediction (MRP), a lightweight module that enables dependency-aware multi-token denoising within a single backbone forward pass. MRP exploits a key property of the denoising process: the logit distributions at adjacent denoising steps are remarkably similar. Rather than running the backbone a second time to obtain the next-step logits, MRP predicts the residual between steps from the backbone's hidden states, effectively denoising more tokens per backbone forward at a fraction of the cost. We apply MRP across the two operating regimes of DLM decoding. In the high-quality-low-throughput static denoising regime, MRP serves as a drafter for speculative decoding: its proposals are verified against the backbone, yielding lossless acceleration of up to 1.4x in SGLang. In the low-quality-high-throughput dynamic denoising regime, MRP instead drives a remasking scheme that revokes over-eager reveals, recovering most of the accuracy lost to aggressive low-threshold decoding and improving accuracy by up to 22.6 points on code generation task HumanEval and 17.7 points on reasoning task GSM8K.

Diffusion Language Models (DLMs) have recently emerged as a promising alternative to autoregressive language models, offering stronger global awareness and highly parallel generation. However, post-training DLMs with standard Negative Evidence Lower Bound (NELBO)-based supervised fine-tuning remains inefficient: training reconstructs randomly masked tokens in a single step, whereas inference follows a confidence-guided, multi-step easy-to-hard denoising trajectory. Recent trajectory-based self-distillation methods exploit such inference trajectories mainly for sampling-step compression and acceleration, often improving decoding efficiency without substantially enhancing the model's underlying capability, and may even degrade performance under full diffusion decoding. In this work, we ask whether self-distilled trajectories can be used not merely for faster inference, but for genuine knowledge acquisition. Although these trajectories lie on the pretrained DLM's own distributional manifold and thus offer a potentially lower optimization barrier, we find that naively fine-tuning on them with standard NELBO objectives yields only marginal gains. To address this limitation, we propose \textbf{T}rajectory-\textbf{A}ligned optimization via \textbf{Bo}ltzmann \textbf{M}odeling (\textbf{TABOM}), a self-distilled trajectory-based post-training framework that aligns training with the easy-to-hard structure of inference. TABOM models the inference unmasking preference as a Boltzmann distribution over predictive entropies and derives a tractable pairwise ranking objective to align the model's certainty ordering with the observed decoding trajectory. Empirically, TABOM achieves substantial gains in new domains, expands the effective knowledge boundary of DLMs, and significantly mitigates catastrophic forgetting compared with standard SFT.

Recently, reinforcement learning (RL) has been widely applied during post-training for diffusion large language models (dLLMs) to enhance reasoning with block-wise semi-autoregressive generation. Block size has therefore become a vital factor in dLLMs, since it determines the parallel decoding granularity and affects the rollout trajectories during RL optimisation, e.g., GRPO. Instead of investigating the effect of block size during inference on individual domains, this paper studies block size from a domain conflict perspective for dLLM RL post-training in multi-domain scenarios. The main contributions are: (1) a formulation of domain block size conflict in multi-domain RL for dLLMs, which will largely affect the post-training effectiveness for rollout-based RL methods; (2) a novel dataset, Block-R1-41K is constructed with a best-improved training block size for each sample, which also induces a Block Size Conflict Score to quantitatively measure the domain conflict; (3) a new benchmark, Block-R1, for flexible RL post-training for dLLMs in both single and cross domain; and (4) a simple yet powerful cross-domain post-training method with sample-level best-improved training block sizes. Extensive experiments on 13 distinct datasets, 7 latest RL algorithms and diverse dLLM backbones are comprehensively covered in Block-R1. The benchmark is open-sourced at https://github.com/YanJiangJerry/Block-R1 with the dataset released at https://huggingface.co/datasets/YanJiangJerry/Block-R1-41K.

Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities. However, for tractability, discrete diffusion models sample from a factorized distribution, which is less expressive than AR. Recent Flow Language Models (FLMs) apply continuous flows to language, transporting noise to data with a deterministic ODE that avoids factorized sampling. FLMs operate on one-hot vectors whose dimension scales with the vocabulary size, making FLMs costly to train. Moreover, since all distinct one-hot embeddings are equidistant in $\ell_2$, adding Gaussian noise does not have a clear semantic interpretation (unlike images, where Gaussian noise progressively degrades structure). We introduce $\mathbb{S}$-FLM, a latent FLM in the hypersphere. $\mathbb{S}$-FLM generates sequences by rotating vectors in $\mathbb{S}^{d-1}$ along a velocity field learned with cross-entropy, avoiding the overhead of materializing one-hot vectors. Previous FLMs match AR in Generative Perplexity (Gen.\ PPL), but samples with high likelihood are not necessarily correct in verifiable domains such as math and code. $\mathbb{S}$-FLM substantially improves continuous flow language models on large-vocabulary reasoning and closes the gap to masked diffusion under standard-temperature sampling ($T=1$), while a gap remains under optimized low-temperature ($T=0.1$) decoding.

Diffusion and flow-based models have become the de facto approaches for generating continuous data, e.g., in domains such as images and videos. Their success has attracted growing interest in applying them to language modeling. Unlike their image-domain counterparts, today's leading diffusion language models (DLMs) primarily operate over discrete tokens. In this paper, we show that continuous DLMs can be made effective with minimal adaptation to the discrete domain. We propose Embedded Language Flows (ELF), a class of diffusion models in continuous embedding space based on continuous-time Flow Matching. Unlike existing DLMs, ELF predominantly stays within the continuous embedding space until the final time step, where it maps to discrete tokens using a shared-weight network. This formulation makes it straightforward to adapt established techniques from image-domain diffusion models, e.g., classifier-free guidance (CFG). Experiments show that ELF substantially outperforms leading discrete and continuous DLMs, achieving better generation quality with fewer sampling steps. These results suggest that ELF offers a promising path toward effective continuous DLMs.

Masked Diffusion Models (MDMs) have emerged as a promising alternative to autoregressive models in language modeling, offering the advantages of parallel decoding and bidirectional context processing within a simple yet effective framework. Specifically, their explicit distinction between masked tokens and data underlies their simple framework and effective conditional generation. However, MDMs typically require many sampling iterations due to factorization errors stemming from simultaneous token updates. We observe that a theoretical lower bound of the factorization error exists, which standard MDMs cannot reduce due to their use of a deterministic single-state mask. In this paper, we propose the Infinite Mask Diffusion Model (IMDM), which introduces a stochastic infinite-state mask to mitigate the theoretical bound while directly inheriting the benefits of MDMs, including the compatibility with pre-trained weights. We empirically demonstrate that MDM fails to perform few-step generation even in a simple synthetic task due to the factorization error bound, whereas IMDM can find an efficient solution for the same task. Finally, when equipped with appropriate distillation methods, IMDM surpasses existing few-step distillation methods at small step counts on LM1B and OpenWebText. Code is available at https://Ugness.github.io/official_imdm.

Diffusion large language models (dLLMs) offer a promising route to parallel and efficient text generation, but improving their reasoning ability requires effective post-training. Reinforcement learning with verifiable rewards (RLVR) is a natural choice for this purpose, yet its application to dLLMs is hindered by the absence of tractable sequence-level log-ratios, which are central to standard policy optimization. The lack of tractable sequence-level log-ratios forces existing methods to rely on high-variance ELBO-based approximations, where high verifier rewards can amplify inaccurate score estimates and destabilize RL training. To overcome this issue, we propose \textbf{R}elative \textbf{S}core \textbf{P}olicy \textbf{O}ptimization (RSPO), a simple RLVR method that uses verifiable rewards to calibrate noisy likelihood estimates in dLLMs. The core of our algorithm relies on a key observation: a reward advantage can be interpreted not only as an update direction, but also as a target for the relative log-ratio between the current and reference policies. Accordingly, RSPO calibrates this noisy relative log-ratio estimate by comparing its reward advantage with the reward-implied target relative log-ratio, updating the policy according to the gap between the current estimate and the target rather than the raw advantage alone. Experiments on mathematical reasoning and planning benchmarks show that RSPO yields especially strong gains on planning tasks and competitive mathematical-reasoning performance.

Generating high-fidelity synthetic GPS trajectories is increasingly important for applications in transportation, urban planning, and what-if scenario simulation, especially as privacy concerns limit access to real-world mobility data. Existing trajectory generation models face a trade-off between efficiency and faithfulness to road network topology: continuous-space methods enable fast generation but ignore the road network, while topology-aware approaches rely on search-based autoregressive decoding that limits generation speed. We propose TrajDLM, a topology-aware trajectory generation framework based on block diffusion language models that bridges this gap. TrajDLM models trajectories as sequences of discrete road segments, combining a block diffusion backbone for efficient denoising, topology-aware embeddings from a road network encoder, and topology-constrained sampling to ensure coherent and realistic trajectories. Across three city-scale datasets, TrajDLM achieves strong performance on fine-grained local similarity metrics while being up to $2.8\times$ faster than prior work, and demonstrates strong zero-shot transfer across domains, including unseen transportation modes. These results highlight the effectiveness of block-wise discrete diffusion as a scalable approach to accurate and efficient trajectory generation. Our code is available at https://github.com/cruiseresearchgroup/TrajDLM/

Diffusion language models (DLMs) have recently emerged as a promising alternative to autoregressive models, primarily due to their ability to enable parallel decoding. Despite this advantage, most existing DLMs rely on a fixed generation length specified prior to decoding, which restricts their flexibility in real-world applications. While a few recent works attempt to support flexible-length generation, they typically suffer from notable limitations: some require costly retraining to accommodate variable-length outputs, while others depend solely on local confidence signals during decoding. Such local criteria fail to capture the evolving structure of the sequence, often resulting in suboptimal generation quality. In this paper, we propose a training-free, Bayesian structured decoding framework that formulates flexible-length generation as a dynamic structural inference problem. Our approach formulates flexible-length generation as a dynamic structural inference problem, jointly computing the expansion length, the block boundaries, and the decoding schedule. At each window expansion step, the method integrates local uncertainty with structural signals via a unified mechanism that supports dynamic structured generation, including both flexible block expansion and block organization, while maintaining coherence. Extensive experiments across multiple benchmarks demonstrate that our approach significantly improves generation quality and flexibility over existing fixed-length and flexible-length baselines. These results highlight the advantage of Bayesian structured decoding for diffusion language model, providing a principled and efficient solution for structured text generation.

Masked diffusion language models enable parallel token generation and offer improved decoding efficiency over autoregressive models. However, their performance degrades significantly when generating multiple tokens simultaneously, due to a mismatch between token-level training objectives and joint sequence consistency. In this paper, we propose ME-DLM, an edit-based refinement framework that augments diffusion generation with lightweight post-editing steps. After producing an initial complete response, the model refines it through minimal edit operations, including replacement, deletion, and insertion, conditioned on the full sequence. Training supervision is derived from edit distance, providing a deterministic signal under a fixed canonicalization scheme for learning minimal corrections. This approach encourages sequence-level consistency through globally conditioned edits while preserving the efficiency benefits of parallel diffusion decoding. Extensive experiments demonstrate that ME-DLM improves the quality and robustness of multi-token parallel generation. In particular, when built upon LLaDA, our method achieves consistent gains of 11.6 points on HumanEval and 33.6 points on GSM8K while using one-eighth of the total diffusion steps. Code is available at https://github.com/renhouxing/ME-DLM.

Diffusion large language models (dLLMs) offer a promising paradigm for parallel text generation, but in practice they face an accuracy-parallelism trade-off, where increasing tokens per forward (TPF) often degrades generation quality. Existing acceleration methods often gain speed at the cost of accuracy. To address this limitation, we propose TAD, a Temporal-Aware trajectory self-Distillation framework. During data construction, we condition a teacher model on both the prompt and the ground-truth response to generate decoding trajectories, recording the intermediate masked states throughout the process. Based on how many decoding steps remain before each masked token is revealed, we partition masked positions into near and distant subsets. For near tokens, we train the student with a hard cross-entropy loss using the teacher trajectory tokens as labels, encouraging confident predictions for tokens that are about to be decoded. For distant tokens, we apply a soft KL divergence loss between the teacher and student token distributions, providing softer supervision and preserving future planning knowledge. This temporal-aware partition naturally gives rise to two deployment configurations: a Quality model that prioritizes accuracy and a Speed model that favors more aggressive acceleration. Experiments show that TAD consistently improves the accuracy-parallelism trade-off. On LLaDA, it raises average accuracy from 46.2% to 51.6% with the Quality model and average AUP from 46.2 to 257.1 with the Speed model. Our code is available at: https://github.com/BHmingyang/TAD

Diffusion language models (DLMs) offer a structural alternative to autoregressive generation: denoising can update tokens in arbitrary orders or in parallel rather than along a fixed left-to-right chain. In practice, fast DLM decoding remains strongly order-sensitive and often drifts toward autoregressive-like trajectories. We trace this tension to compatibility. At each reverse-time step, a DLM provides local denoising conditionals over the unresolved tokens. Arbitrary-order denoising becomes well defined when these local conditionals compose into order-invariant pseudo-joints. We formalize this view by defining order-induced pseudo-joints and a local denoising circulation: the log-ratio between the two pseudo-joints obtained by swapping a pair of unresolved positions. This circulation is zero under compatible conditionals, and global order gaps decompose into sums of local circulations along adjacent swaps. We further separate incompatibility-driven path dependence from conditional-dependence error in parallel updates and from order-specific estimation error. The resulting framework provides inference-only diagnostics for testing when DLM decoding is genuinely order-free.

Diffusion Language Models (dLLMs) have garnered significant attention for their potential in highly parallel processing. The parallel capabilities of existing dLLMs stem from the assumption of conditional independence at high confidence levels, which ensures negligible discrepancy between the marginal and joint distributions. However, the stringent confidence thresholds required to preserve accuracy severely constrain the scalability of parallelism. Through systematic token-level statistical analysis, we reveal that a substantial proportion of tokens converge to their correct predictions early in the denoising process yet fail to reach standard confidence thresholds, confirming that current confidence-based criteria are overly conservative. In response, we introduce LEAP (Lookahead Early-Convergence Token Detection for Accelerated Parallel Decoding). LEAP is a training-free, plug-and-play method that leverages future context filtering and multi-sequence superposition to detect early-converging tokens. By validating the alignment between early convergence and correctness, we enable reliable early decoding of these tokens. Benchmarking across diverse domains demonstrates that LEAP significantly lowers inference latency and decoding steps. Compared to confidence-based decoding, the average number of denoising steps is reduced by about 30%. On the GSM8K dataset, combining LEAP with dParallel accelerates decoding to 7.2 tokens per step while preserving model precision. LEAP effectively breaks the reliance on high-confidence priors, offering a novel paradigm for parallel decoding.

Discrete diffusion language models (DLMs) generate text by iteratively denoising all positions in parallel, offering an alternative to autoregressive models. Controlled generation methods for DLMs, imported from autoregressive models, apply uniform intervention at every denoising steps. We show this uniform schedule degrades quality, and the damage compounds when multiple attributes are steered jointly. To diagnose the failure, we train sparse autoencoders on four DLMs (124M-8B parameters) and find that different attributes commit on distinct schedules, varying in timing, sharpness, and magnitude. For instance, topic commits within the first 2% of denoising, whereas sentiment emerges gradually over 20% of the process. Consequently, uniform intervention wastes steering capacity on steps where the target attribute has already solidified or has yet to emerge. We propose a novel adaptive scheduler that concentrates interventions on the steps where an attribute is actively forming and leaves the rest of generation untouched. The cost-control trade-off admits a closed-form characterization: the advantage of adaptive over uniform scheduling is governed by a single dispersion statistic of the commitment distribution. Across four DLMs and seven steering tasks, our method achieves precise control without the degradation typical of uniform interventions. Especially on challenging simultaneous three-attribute control, it reaches up to 93% steering strength, beating the strongest baseline by up to 15% points while preserving generation quality.

Latent diffusion models offer an attractive alternative to discrete diffusion for non-autoregressive text generation by operating on continuous text representations and denoising entire sequences in parallel. The major challenge in latent diffusion modeling is constructing a suitable latent space. In this work, we present the Latent Diffusion Language Model (LDLM), in which the latent encoder, diffusion model, and decoder are trained jointly. LDLM builds its latent space by reshaping the representations of a pre-trained language model with a trainable encoder, yielding latents that are easy to both denoise and decode into tokens. We show that naive joint training produces a low-quality diffusion model, and propose a simple training recipe consisting of an MSE decoder loss, diffusion-to-encoder warmup, adaptive timestep sampling, and decoder-input noise. Ablations show that each component substantially impacts generation performance. On OpenWebText and LM1B, LDLM achieves better generation performance than existing discrete and continuous diffusion language models while being $2{\text -}13\times$ faster, indicating that jointly learning the latent space is a key step toward making latent diffusion competitive for text generation.

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a few steps. When the student underperforms, the usual explanation is insufficient capacity. We argue the opposite: the trajectory is the bottleneck, not the student. Each training trajectory is built through a chain of blind stochastic jumps with no evaluation of sequence quality; a single bad decision at an early midpoint propagates through subsequent steps, yet the student must imitate the result. Trajectory-Shaped Discrete Flow Matching (TS-DFM) replaces these blind jumps with guided navigation: a lightweight energy compass evaluates candidate continuations at each midpoint, selecting the most coherent. All shaping is training-only; inference cost is unchanged. On 170M-parameter language modeling, the shaped student at 8 steps achieves 32% lower perplexity than the 1,024-step teacher while being 128x faster, with gains consistent across source distributions and three evaluators of increasing scale. TS-DFM achieves the best perplexity of any discrete-generation baseline we compare against, including methods trained on 6x more data or using 5x larger models.

Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including accelerated sampling and tilting. Recently, several works have demonstrated the possibility of generating discrete data continuously by a simple flow matching process between a Gaussian and the one-hot encoded data distribution. They have further shown the feasibility of accelerated sampling via Categorical Flow Maps (CFMs), resulting in competitive sample quality in the few-step regime. However, this method had only been evaluated at relatively modest scales ($<1$B), leaving the question of its scalability completely open. In this article, we train a $1.7$B-parameter base flow model on $2.1$T tokens and self-distill it into a CFM that generates diverse, high-quality text in as few as $4$ inference steps while maintaining near-data-level token entropy. Furthermore, we introduce a likelihood bound for CFMs in the semi-discrete setting, and show that they can be used to score the model on standard LM benchmarks, achieving results in the same range as discrete diffusion methods. Finally, we uncover some of the challenges that arise from training these models at scale, and we provide prescriptive insights on loss weighting and time scheduling.

Diffusion Transformers (DiT) trained with flow matching in a VAE latent space have unified visual generation across images and videos. A natural next step toward a single architecture for both generation (visual synthesis) and understanding (text generation) is to apply this framework to language modeling. We propose TextLDM, which transfers the visual latent diffusion recipe to text generation with minimal architectural modification. A Transformer-based VAE maps discrete tokens to continuous latents, enhanced by Representation Alignment (REPA) with a frozen pretrained language model to produce representations effective for conditional denoising. A standard DiT then performs flow matching in this latent space, identical in architecture to its visual counterpart. The central challenge we address is obtaining high-quality continuous text representations: we find that reconstruction fidelity alone is insufficient, and that aligning latent features with a pretrained language model via REPA is critical for downstream generation quality. Trained from scratch on OpenWebText2, TextLDM substantially outperforms prior diffusion language models and matches GPT-2 under the same settings. Our results establish that the visual DiT recipe transfers effectively to language, taking a concrete step toward unified diffusion architectures for multimodal generation and understanding.

Diffusion Vision-Language Models (dVLMs), built upon the non-causal foundations of Diffusion Large Language Models (dLLMs), have demonstrated remarkable efficacy in multimodal tasks by departing from the traditional autoregressive generation paradigm. While dVLMs appear inherently robust against conventional jailbreak tactics, which we categorize as Fixed Prefix Optimization (FPO) (e.g., anchoring responses with "Sure, here is"), this perceived resilience is deceptive. Our investigation into the safety landscape of dVLMs reveals a unique refusal pattern: Immediate Refusal and Progressive Refusal. We find that while FPO-based attacks often fail by triggering the latter, the progressive refinement process itself uncovers a novel, latent attack surface. To exploit this vulnerability, we propose Global Probability Optimization (GPO), a general jailbreak paradigm designed specifically for the denoising trajectory of masked diffusion models. Unlike prefix-based methods, GPO manipulates the global generative dynamics to bypass guardrails in diffusion language models. Building on this, we introduce GPO-V, the first visual-modality jailbreak framework tailored for dVLMs. Empirical results demonstrate that GPO-V produces stealthy perturbations with exceptional cross-model transferability, revealing a critical security gap in non-sequential generative architectures. Our findings underscore the critical urgency of addressing safety alignment in dVLMs. These results necessitate an immediate and fundamental re-evaluation of current defense paradigms to mitigate the unique risks of diffusion-based generation. Our code is available at: https://anonymous.4open.science/r/GPO-V-0250.

Cell-level dense prediction is central to computational pathology, but remains challenging due to fine-grained histological structures, strong domain shifts, and costly dense annotations. Existing ViT-based pathology foundation models rely on patch tokenization, which can disrupt spatial continuity and weaken local morphological details needed for cell-level prediction. To address this, we propose Masked-Diffusion Convolutional Foundation Models, termed ConvNeXt Masked-Diffusion (CMD), a self-supervised convolutional generative pretraining framework for dense pathology representation learning. CMD uses a fully convolutional ConvNeXt-UNet backbone, performs masked-diffusion pretraining in pixel space, and incorporates frozen pathology foundation model features through adaptive normalization. Experimental results demonstrate that CMD consistently outperforms existing ViT-based pathology foundation models and even surpasses state-of-the-art end-to-end segmentation methods while fine-tuning only a small number of task-specific parameters across multiple pathology dense prediction tasks. The advantage is particularly pronounced under limited annotation settings, where CMD exhibits stronger robustness and generalization ability. Our findings suggest that purely convolutional architectures can also serve as competitive pathology foundation models for cell-level dense prediction, achieving leading performance within the current ViT-dominated paradigm and providing a scalable, high-performance solution that better preserves histological structural priors for fine-grained pathology understanding.

This paper shows how diffusion language models (DLMs) can be used as effective and efficient retrievers. Existing DLM-based retrievers (e.g., DiffEmbed) follow BERT-style encoding, representing each query or passage as a single mean-pooled vector. This ignores how DLMs are trained to generate responses through masked-position prediction under bidirectional attention, a capability that can provide stronger retrieval signals. We propose DiffRetriever, which uses the DLM's native masked-position prediction directly for retrieval. For each query or passage, DiffRetriever appends one or more masked positions, using the outputs as retrieval representations in a single forward pass. With one masked position, single-representation DiffRetriever already improves over DiffEmbed on the same backbones. DiffRetriever also naturally extends to multi-representation retrieval: DLMs process multiple masked positions jointly, enabling ColBERT-style fine-grained matching with little additional encoding latency. In autoregressive LLM retrievers, the same multi-representation strategy requires sequential decoding and therefore incurs much higher latency. DiffRetriever obtains the strongest aggregate effectiveness within our matched comparison, outperforming DiffEmbed, PromptReps, and RepLLaMA. Masked-position counts selected on training data transfer well across datasets, while per-query variation suggests headroom for adaptive allocation. Code is available at https://github.com/ielab/diffretriever.

Diffusion large language models are a compelling alternative to autoregressive models, yet existing RL methods for diffusion treat all denoising steps as equally important and rely on biased, high-variance likelihood estimates. We identify two fundamental weaknesses: the absence of temporal credit assignment across the denoising trajectory, and the systematic bias of mean-field likelihood estimates used for policy optimization. To address these, we propose Denoising-Aware Credit Assignment for GRPO (DACA-GRPO), a lightweight, plug-and-play enhancement for any GRPO-style trainer. DACA-GRPO introduces two complementary mechanisms: Denoising Progress Scores, which extract per-token importance weights from intermediate predictions at no additional forward cost, and Stratified Masking Likelihood, which partitions token positions into strata so that each token is predicted with most of the sequence as context, reducing the mean-field bias. Applied on top of three GRPO base methods, DACA-GRPO achieves consistent improvements across seven benchmarks spanning mathematical reasoning, code generation, constraint satisfaction, and constrained generation, with gains of up to 5.6pp on math reasoning, 7.4pp on code generation, 36.3pp on constraint satisfaction, and 5.9pp on JSON schema adherence.

Diffusion language models (DLMs) promise parallel, order-agnostic generation, but on standard benchmarks they have historically lagged behind autoregressive models in sample quality and diversity. Recent continuous flow and diffusion approaches have narrowed this gap. In this work, we further close the autoregressive gap by modeling text as a continuous diffusion process over fixed-width binary bitstreams. We refer to the resulting model as CoBit (Continuous Bitstream Diffusion). Our approach represents semantic tokens as analog bit sequences and uses a matched-filter residual parameterization to isolate contextual learning from analytic independent-bit posteriors. Crucially, we adopt a stochastic sampler that applies Langevin-type corrections gated by the entropy-rate profile, concentrating stochasticity in high-information regions while remaining nearly deterministic elsewhere. On LM1B, our 130M-parameter model reaches a generative perplexity (GenPPL) of 59.76 at matched real-data entropy (4.31) using 256 neural function evaluations (NFEs), outperforming prior DLM baselines and reaching the autoregressive reference. On OpenWebText (OWT), our sampler establishes a new continuous-DLM Pareto frontier, achieving GenPPL 27.06 at entropy 5.26 using 4x fewer steps than previous 1024-NFE baselines. Scaling the same recipe to a 462M-parameter model (CoBit-M) further improves the OWT GenPPL-entropy frontier over the 130M model (CoBit-S) and over medium-scale continuous and discrete DLM baselines, reaching GenPPL 19.5 at entropy 5.40, near real-data entropy (5.44), and approaching pretrained GPT-2 Medium over the high-quality region. As an additional benefit, bitstream diffusion removes the O(V) vocabulary scaling bottleneck of standard DLMs: by predicting O(log V) bitwise logits via semantic bit-patching, it lowers memory and raises throughput, a scalable paradigm as vocabulary sizes grow.

Diffusion language models (DLMs) have recently demonstrated capabilities that complement standard autoregressive (AR) models, particularly in non-sequential generation and bidirectional editing. Although recent work has shown that pretrained autoregressive checkpoints can be converted into diffusion language models, existing recipes primarily transfer parameters through continued denoising training with objective- and attention-level modifications. We instead ask whether the internal representation geometry learned by next-token prediction can be explicitly preserved during AR-to-DLM conversion. We hypothesize that much of the semantic structure learned by AR pretraining can transfer across generation orders, and thus DLM training should be viewed as relearning the decoding path rather than relearning language representations. To investigate this, we introduce REPR-ALIGN, a representation alignment objective that adapts a bidirectional masked diffusion model to reuse representations from a pretrained AR model of identical architecture. Concretely, we align the hidden states of the DLM to the frozen AR model at every layer using cosine similarity, while optimizing the standard masked denoising objective. This simple alignment, with no adapters and no architectural changes beyond the attention mask, yields up to 4x training acceleration in our setting and is particularly effective in low-data regimes. Our results suggest that linguistic representations can transfer across generation order, and that representation alignment provides a simple and effective technique for training diffusion language models. Code is available at https://github.com/pengzhangzhi/Open-dLLM.

Large language models have achieved remarkable success under the autoregressive paradigm, yet high-quality text generation need not be tied to a fixed left-to-right order. Existing alternatives still struggle to jointly achieve generation efficiency, scalable representation learning, and effective global semantic modeling. We propose Cola DLM, a hierarchical latent diffusion language model that frames text generation through hierarchical information decomposition. Cola DLM first learns a stable text-to-latent mapping with a Text VAE, then models a global semantic prior in continuous latent space with a block-causal DiT, and finally generates text through conditional decoding. From a unified Markov-path perspective, its diffusion process performs latent prior transport rather than token-level observation recovery, thereby separating global semantic organization from local textual realization. This design yields a more flexible non-autoregressive inductive bias, supports semantic compression and prior fitting in continuous space, and naturally extends to other continuous modalities. Through experiments spanning 4 research questions, 8 benchmarks, strictly matched ~2B-parameter autoregressive and LLaDA baselines, and scaling curves up to about 2000 EFLOPs, we identify an effective overall configuration of Cola DLM and verify its strong scaling behavior for text generation. Taken together, the results establish hierarchical continuous latent prior modeling as a principled alternative to strictly token-level language modeling, where generation quality and scaling behavior may better reflect model capability than likelihood, while also suggesting a concrete path toward unified modeling across discrete text and continuous modalities.

Diffusion language models (DLMs) have recently emerged as competitive alternatives to autoregressive (AR) language models, yet differences in their activation dynamics remain poorly understood. We characterize these dynamics in LLaDA-8B and identify a striking layer-collapse property: a few early layers exhibit highly similar, collapsed activation patterns dominated by a single large super-outlier persisting over a long token range. Despite its apparent redundancy, this outlier is critical: pruning it causes outputs to degrade into repetitive random token loops. Paradoxically, layers in LLaDA contain more redundant representations overall, with redundancy most pronounced in earlier layers -- the reverse of AR models, where deeper layers grow redundant due to undertraining. Our analysis indicates that layer collapse in DLMs is not driven by undertraining but by overtraining: a dominant outlier becomes an indispensable information carrier while remaining representations collapse into redundant structure. These findings have strong practical implications, verified through controlled pre-training experiments. DLMs are surprisingly robust to compression: LLaDA under 3-bit GPTQ quantization drops only -1.8% on GSM8K, whereas Llama-3.1-8B drops -64.7%. Optimal sparsity allocation also reverses between families: at 50% average sparsity, allocating more to early layers in LLaDA yields +8.4% over the reverse strategy, while the same allocation costs Llama -8.4%. Our findings reveal that the DLM training objective fundamentally reshapes layer dynamics relative to AR models, with direct consequences for compression and deployment. Code: github.com/Conzel/super-outlier-dlm.

Statistical watermarking is a common approach for verifying whether text was written by a language model. Most existing schemes assume autoregressive generation, where tokens are produced left to right and contextual hashing is well defined. Diffusion language models generate text by denoising tokens in arbitrary order, so these schemes cannot be applied directly. A recent watermark by Gloaguen et al. addresses this gap for LLaDA 8B Instruct and reports true positive detection above 99%. This paper studies what happens when watermarked text is rewritten not once but several times. Using the same watermark configuration, 1,605 watermarked completions of about 300 tokens each are produced across five WaterBench domains. Each completion is rewritten by four open weight language models, from 1.5B to 8B parameters, none of which know the watermark key. Five rewrite styles are tested: paraphrase, humanize, simplify, academic, and summarize expand. Each style is chained for up to five hops, producing 160,500 rewritten texts in total. The watermark is detected on 87.9% of the original outputs at the standard significance threshold. After a single rewrite, detection falls to between 14% and 41% depending on the rewriter and style. After five chained rewrites, detection falls to 4.86%, meaning 94.76% of the originally detected texts are no longer flagged. After three rewrites, the detector score has dropped 86% of the way from its watermarked baseline toward the null distribution. Repeated rewriting is therefore a much stronger attack than a single rewrite, and the result holds across all four rewriters tested.

We present a discrete diffusion-based language model using Glauber dynamics from statistical physics. Our main insight is that instead of trying to train a discrete state space diffusion model using Glauber dynamics with a uniform transition kernel as the forward process, one can set up an ``energy function'' based on pretrained causal/masked language models. When viewed as the stationary distribution, this energy function allows us to significantly improve the quality of the generated text. Incorporating UL2 as the pretrained model into our diffusion pipeline, we outperform prior diffusion based LMs and perform competitively with autoregressive models of comparable model sizes. Furthermore, our models are competitive with or outperform prior diffusion models and GPT-2 style auto-regressive models on zero-shot common sense reasoning tasks as well as planning and search tasks like Sudoku and Zebra puzzles.

Diffusion-based Large Language Models (D-LLMs) represent a promising frontier in generative AI, offering fully parallel token generation that can lead to significant throughput advantages and superior GPU utilization over the traditional autoregressive paradigm. However, this parallelism is constrained by the requirement of a fixed-size response length prior to generation. This architectural limitation imposes a severe trade-off: oversized response length results in computational waste on semantically meaningless padding tokens, while undersized response length causes output truncation requiring costly re-computations that introduce unpredictable latency spikes. To tackle this issue, we propose Predict-then-Diffuse, a simple and model-agnostic framework that enables compute-budgeted inference per input query by first estimating the response length and then using it to run inference with D-LLM. At its core lies an Adaptive Response Length Predictor (AdaRLP), which estimates the optimal response length given an input query. As a measure against under-estimating the response length and re-running inference with a higher value, we introduce a data-driven safety mechanism based on a small increase of the predicted length. As a whole, our framework avoids wasting computation on padding tokens, at the same time preserving output quality. Experimental validation on multiple datasets demonstrates that Predict-then-Diffuse significantly reduces computational costs (FLOP) compared to the default D-LLM inference mechanism, while being robust to skewed data distributions.

Dynamic point cloud pretraining is still dominated by masked reconstruction objectives. However, these objectives inherit two key limitations. Existing methods inject ground-truth tube centers as decoder positional embeddings, causing spatio-temporal positional leakage. Moreover, they supervise inter-frame motion with deterministic proxy targets that systematically discard distributional structure by collapsing multimodal trajectory uncertainty into conditional means. To address these limitations, we propose Diffusion Masked Pretraining (DiMP), a unified self-supervised framework for dynamic point clouds. DiMP introduces diffusion modeling into both positional inference and motion learning. It first applies forward diffusion noise only to masked tube centers, then predicts clean centers from visible spatio-temporal context. This removes positional leakage while preserving visible coordinates as clean temporal anchors. DiMP also reformulates point-wise inter-frame displacement supervision as a DDPM noise-prediction objective conditioned on decoded representations. This design drives the encoder to target the full conditional distribution of plausible motions under a variational surrogate, rather than collapsing to a single deterministic estimate. Extensive experiments demonstrate that DiMP consistently improves downstream accuracy over the backbone alone, with absolute gains of 11.21% on offline action segmentation and 13.65% under causally constrained online inference.Codes are available at https://github.com/InitalZ/DiMP.git.

Recent diffusion large language models (dLLMs) have demonstrated both effectiveness and efficiency in reasoning via a block-based semi-autoregressive generation paradigm. Despite their progress, the fixed-size block generations remain a critical bottleneck for effective and coherent reasoning. 1. From a global perspective, different reasoning tasks would correspond to different optimal decoding block sizes, which makes a ``one-size-fits-all'' assumption ineffective. 2. Even within a single reasoning task, the rigid block partitioning would break the logical flow and reduce reasoning coherence. Through empirical observations, we reveal that for block-wise entropy, incorrect reasoning exhibits a fluctuating and unsteady trend between blocks, whereas the correctly generated tasks follow a consistent descending trend. Therefore, this paper proposes b1, a novel post-training framework for dLLMs that learns dynamic-size reasoning blocks via a Monotonic Entropy Descent objective with reinforcement learning to enhance reasoning coherence.b1 integrates seamlessly as a plug-and-play module with existing dLLM's post-training algorithms. Extensive experiments across various reasoning benchmarks showcase b1's consistent improvement over existing fixed-size block baselines. Our code has been released at https://github.com/YanJiangJerry/Block-R1.

The iterative denoising paradigm of Diffusion Large Language Models (DLMs) endows them with a distinct advantage in global context modeling. However, current decoding strategies fail to leverage this capability, typically exhibiting a local preference that overlooks the heterogeneous information density within the context, ultimately degrading generation quality. To address this limitation, we systematically investigate high-information-density (HD) tokens and present two key findings: (1) explicitly conditioning on HD tokens substantially improves output quality; and (2) HD tokens exhibit an early-decoding tendency, converging earlier than surrounding tokens. Motivated by these findings, we propose Focus on the Core \textbf{(FoCore)}, a training-free decoding strategy that utilizes HD tokens in a self-contrast manner, wherein HD tokens are temporarily remasked as negative samples, to guide generation. We further introduce FoCore_Accelerate \textbf{(FoCore_A)}, an efficient variant that, upon detecting HD token convergence, performs parallel decoding over stable candidates within a local context window, substantially accelerating generation. Extensive experiments on math, code and logical reasoning benchmarks demonstrate that FoCore consistently improves generation quality and efficiency across both LLaDA and Dream backbones. For instance, on HumanEval, FoCore improves pass@1 from 39.02 to 42.68 over standard Classifier-Free Guidance, while FoCore-A reduces the number of decoding steps by 2.07x and per-sample latency from 20.76s to 8.64s (-58.4%).

Diffusion Large Language Models (dLLMs) have emerged as a promising alternative to auto-regressive (AR) models, offering greater expressive capacity and potential for parallel generation and faster inference. However, open-source dLLMs remain immature, lagging behind AR models in both efficiency and quality. We identify an underexplored property of dLLMs: token-wise redundancy in bi-directional self-attention. Self-attention activations are highly correlated across tokens, and temporal changes in query representations can predict redundancy in corresponding key, value, and output activations. We introduce DARE, with two complementary mechanisms: DARE-KV, which reuses cached key-value (KV) activations, and DARE-O, which reuses output activations to reduce redundant computation while preserving quality. DARE achieves up to 1.20x per-layer latency reduction and reuses up to 87% of attention activations, with negligible degradation on reasoning and code-generation benchmarks. DARE-KV and DARE-O incur average performance drops of only 2.0% and 1.2%, respectively. Combined with techniques such as prefix caching and Fast-dLLM, DARE provides additive gains without retraining. These results establish token-wise reuse as an effective strategy for improving the efficiency of diffusion-based LLMs while preserving generation fidelity. Code: https://github.com/enyac-group/DARE

Proteins are shaped by gradual evolution under biophysical and functional constraints. Protein language models learn rich evolutionary constraints from large-scale sequences, and discrete diffusion-based protein language models~(\eg, DPLMs) are promising for both understanding and generation. However, existing DPLMs typically rely on masked diffusion that contradicts a simple biological intuition: proteins evolve through accumulated edits, not by emerging from masks. Consequently, these frameworks lack explicit pretraining objectives for substitution and insertion/deletion (indel) operations, limiting both optimization-style post-editing and flexible guided generation. To address these limitations, we present DPLM-Evo, an evolutionary discrete diffusion framework that explicitly predicts substitution, insertion, and deletion operations during denoising. DPLM-Evo decouples an upsampled-length latent alignment space from the variable-length observed sequence space, which makes indel-aware generation tractable. To better align substitutions with real evolution, we further introduce a contextualized evolutionary noising kernel that produces biologically informed, context-dependent mutation patterns. Across tasks, DPLM-Evo improves sequence understanding and achieves state-of-the-art mutation effect prediction performance on ProteinGym in the single-sequence setting. It also enables variable-length simulated evolution, and post-editing/optimization of existing proteins via explicit edit trajectories.

Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps. In continuous domains, consistency training along the probability-flow ODE is a popular recipe to accelerate diffusion. For discrete diffusion, no analogous sample-space ODE exists, making direct adaptation ill-defined. We argue that the right discrete substitute is the exact posterior bridge, the closed-form conditional law linking any two noise levels, which is available for broad corruptions including masked and uniform diffusion. Building on this observation, we introduce Multi-Path Discrete Consistency (MPDC), a new principle that trains a denoiser to be path-invariant in expectation across these stochastic bridges, and instantiate it as the Consistent Diffusion Language Model (CDLM), a single-stage training framework that does not require an already trained teacher model. Our CDLM objective recovers masked diffusion, continuous consistency models, and progressive or discrete distillation as analytic limits or empirical approximations of one common view. Empirically, CDLM establishes a new state of the art on both conditional and unconditional text-generation, consistently outperforming strong base discrete diffusion models and often even multi-stage distilled baselines across sampling budgets, with the largest gains in the few-step regime. Together, these results position CDLM as a principled and scalable foundation for the next generation of fast, high-fidelity discrete generative modeling.

Diffusion large language models (dLLMs) offer parallel decoding and bidirectional context, but state-of-the-art dLLMs require billions of parameters for competitive performance. While existing distillation methods for dLLMs reduce inference steps within a single architecture, none address cross-architecture knowledge transfer, in which the teacher and student differ in architecture, attention mechanism, and tokenizer. We present TIDE, the first framework for cross-architecture dLLM distillation, comprising three modular components: (1) TIDAL, which jointly modulates distillation strength across training progress and diffusion timestep to account for the teacher's noise-dependent reliability; (2) CompDemo, which enriches the teacher's context via complementary mask splitting to improve predictions under heavy masking; and (3) Reverse CALM, a cross-tokenizer objective that inverts chunk-level likelihood matching, yielding bounded gradients and dual-end noise filtering. Distilling 8B dense and 16B MoE teachers into a 0.6B student via two heterogeneous pipelines outperforms the baseline by an average of 1.53 points across eight benchmarks, yielding notable gains in code generation, where HumanEval scores reach 48.78 compared to 32.3 for the AR baseline.

When do language diffusion models memorize their training data, and how to quantitatively assess their true generative regime? We address these questions by showing that Uniform-based Discrete Diffusion Models (UDDMs) fundamentally behave as Associative Memories (AMs) $\textit{with emergent creative capabilities}$. The core idea of an AM is to reliably recover stored data points as $\textit{memories}$ by establishing distinct basins of attraction around them. Historically, models like Hopfield networks use an explicit energy function to guarantee these stable attractors. We broaden this perspective by leveraging the observation that energy is not strictly necessary, as basins of attraction can also be formed via conditional likelihood maximization. By evaluating token recovery of $\textit{training}$ and $\textit{test}$ examples, we identify in UDDMs a sharp memorization-to-generalization transition governed by the size of the training dataset: as it increases, basins around training examples shrink and basins around unseen test examples expand, until both later converge to the same level. Crucially, we can detect this transition using only the conditional entropy of predicted token sequences: memorization is characterized by vanishing conditional entropy, while in the generalization regime the conditional entropy of most tokens remains finite. Thus, conditional entropy offers a practical probe for the memorization-to-generalization transition in deployed models.

Recent work on text diffusion models offers a promising alternative to autoregressive generation, but controlling their safety remains underexplored. Existing safety approaches are geared toward autoregressive models and typically rely on post-hoc filtering or inference-time interventions. These are inadequate for effectively addressing safety risks in text diffusion models. We propose the Safety-Aware Denoiser (SAD), a safety-guidance framework in text diffusion models. The SAD modifies the iterative denoising process such that the text sample at the final denoising step is steered toward provably safe regions of the text space. This inference-time method can integrate safety constraints into the denoiser, avoiding computationally expensive retraining of the underlying diffusion model and enabling flexible, lightweight safety guidance. We evaluate the safety of the generated text using the SAD, with respect to hazard taxonomy, memorization, and jailbreak. Experimental results show that SAD substantially reduces unsafe generations while preserving generation quality, diversity, and fluency, outperforming existing methods. These results demonstrate that our safety guidance during denoising provides an effective and scalable mechanism for enforcing safety in text diffusion models.

Speech-only spoken language models (SLMs) lag behind text and text-speech models in performance, with recent discrete autoregressive (AR) SLMs indicating significant computational and data demands to match text models. Since discretizing continuous speech for AR creates bottlenecks, we explore whether continuous diffusion (CD) SLM is more viable. To quantify the SLMs linguistic quality, we introduce the phoneme Jensen-Shannon divergence (pJSD) metric. Our analysis reveals CD SLMs, mirroring AR behavior, exhibit scaling laws for validation loss and pJSD, and show optimal token-to-parameter ratios decreasing as compute scales. However, for the latter, loss becomes insensitive to choice of data and model sizes, showing potential for fast inference. Scaling CD SLMs to 16B parameters with tens of millions of hours of conversational data enables generation of emotive, prosodic, multi-speaker, multilingual speech, though achieving long-form coherence remains a significant challenge.

Diffusion language models generate without a fixed left-to-right order, leaving token ordering as a central algorithmic choice. Existing systems mainly use random masking or confidence-driven ordering, which respectively suffer from train--test mismatch and myopic exploration. We introduce DPRM (Doob -transform Process Reward Model), a plug-in token-ordering module that keeps the host architecture, denoising objective and supervision unchanged, and modifies only the ordering policy. DPRM starts from confidence-driven ordering and gradually shifts to process-reward-guided ordering through online estimates. We characterize the exact DPRM policy as a reward-tilted Gibbs reveal law, prove convergence of its stagewise Soft-BoN approximation, show that the online bucketized controller tracks the exact DPRM score at empirical-Bernstein rates, and establish a sample-complexity advantage under tractable optimization assumptions. Across nine hosts covering language reasoning, test-time scaling, protein, single-cell, molecular, DNA, text-to-image generation, and VQA, DPRM order variants improve several language, DNA, and multimodal settings while also identifying boundary cases where confidence-only ordering or task-specific utilities are preferable. Code is available at: https://github.com/DakeBU/DPRM-DLLM

Fine-tuned autoregressive models for graph-to-sequence generation (G2S) often struggle with factual grounding and edit sensitivity. To tackle these issues, we propose a non-autoregressive diffusion framework that generates text by iterative refinement conditioned on an input graph, named as Diffusion Language Model for Graphs (DLM4G). By aligning graph components (entities/relations) with their corresponding sequence tokens, DLM4G employs an adaptive noising strategy. The proposed strategy uses per-token denoising error as a signal to adaptively modulate noise on entity and relation tokens, improving preservation of graph structure and enabling localized updates under graph edits. Evaluated on three datasets, DLM4G consistently outperforms competitive G2S diffusion baselines trained on identical splits across both surface-form and embedding-based metrics. DLM4G further exceeds fine-tuned autoregressive baselines up to 12x larger (e.g., T5-Large) and is competitive with zero-shot LLM transfer baselines up to 127x larger. Relative to the strongest fine-tuned PLM baseline, DLM4G improves factual grounding (FGT@0.5) by +5.16% and edit sensitivity (ESR) by +7.9%; compared to the best diffusion baseline, it yields gains of +3.75% in FGT@0.5 and +23.6% in ESR. We additionally demonstrate applicability beyond textual graphs through experiments on molecule captioning, indicating the method's generality for scientific G2S generation.

Discrete diffusion language models (dLLMs) enable parallel token updates with bidirectional attention, yet practical generation typically adopts blockwise semi-autoregressive decoding. This switch creates a training-inference mismatch: training denoises with full-sequence context, while inference commits tokens within a bounded block without future context. Therefore, decoding with fixed-size or heuristic-based blocks can lead to premature token commitments, as decisions are made without full access to future context that could alter those choices. Motivated by this, we propose self-containedness as a principled criterion for block commitment. A block is self-contained if its predictions remain consistent with Future-Aware (FA) or without No-Future (NF) access to future context, reframing block boundary selection as a test of self-containedness rather than a heuristic choice. Based on this principle, we introduce Variable-size Self-contained Blocks (VSB) for dLLMs. VSB scores and selects block boundaries using the divergence between token-level predictive distributions under NF and FA conditioning, which quantifies how predictions would change if future context were revealed. We provide theoretical justification linking self-containedness to predictive consistency, and extensive experiments validate VSB's efficacy over fixed-size and heuristic blockwise decoding.

While In-Context Learning (ICL) is extensively studied in Autoregressive (AR) LLMs, its mechanism within Diffusion Large Language Models (dLLMs) remains largely unexplored. Unlike AR models restricted by unidirectional causal masking, dLLMs intrinsically utilize bidirectional attention, offering extensive spatial flexibility for query placement. Unfortunately, current practices conventionally inherit AR-style trailing-query templates, often overlooking the structural paradigm shift. This paper presents a comprehensive analysis unveiling that query position is actually a first-order variable in dLLMs. Through empirical decoupling, we demonstrate that positional variance impacts generation quality on par with example semantic quality. Internally, this positional sensitivity stems from a spatial ``Recency Effect'' in attention flow and task-dependent shifts in decoding trajectories. To mitigate this instability without ground-truth labels, we reveal that traditional single-step confidence ($C_{decoded}$) fails in dLLMs. Instead, we propose Average Confidence ($\overline{C}$), a novel metric tracking the iterative decoding process. By establishing the foundational spatial ICL baselines, we introduce Auto-ICL, a training-free adaptive routing strategy that dynamically optimizes query placement, robustly approaching oracle performance across heterogeneous reasoning and perception tasks.

Diffusion language models expose an explicit denoising trajectory, making it possible to ask when different kinds of information become measurable during generation. We study three independent 32-step runs of LLaDA-8B-Base on masked WikiText-103 text, each with 1{,}000 probe-training sequences and 200 held-out evaluation sequences. From saved trajectories, we derive four temporal measurements: token commitment; linear recoverability of part-of-speech (POS), coarse semantic category, and token identity; confidence and entropy dynamics; and sensitivity under mid-trajectory re-masking. Across seeds, the same ordering recurs: content categories stabilize earlier than function-heavy categories, POS and coarse semantic labels remain substantially more linearly recoverable than exact lexical identity under our probe setup, uncertainty remains higher for tokens that ultimately resolve incorrectly even though late confidence becomes less calibrated, and perturbation sensitivity peaks in the middle of the trajectory. A direct/collateral decomposition shows that this peak is overwhelmingly local to the perturbed positions themselves. In this LLaDA+WikiText setting, denoising time is therefore a useful analysis axis: under our measurements, coarse labels are recovered earlier and more robustly than lexical identity, trajectory-level uncertainty tracks eventual correctness, and mid-trajectory states are the most intervention-sensitive.

Auto-regressive Large Language Models (LLMs) achieve strong performance on coding tasks, but incur high memory and inference costs. Diffusion-based language models (d-LLMs) offer bounded inference cost via iterative denoising, but their behavior under post-training quantization (PTQ) has been sparsely explored. We investigate the application and robustness of PTQ techniques, specifically GPTQ and a modified Hessian-Aware Quantization (HAWQ) algorithm, on a diffusion-based coding LLM (CoDA) and observe that these methods applied to CoDA exhibit greater robustness at low bitwidths compared to Qwen3-1.7B, its auto-regressive counterpart, under a standardized evaluation pipeline. We find that in our setup, CoDA exhibits greater robustness at low bitwidths (2-4 bits), with smaller accuracy degradation across HumanEval and MBPP benchmarks. Additionally, mixed-precision configurations derived from HAWQ provide smooth trade-offs across accuracy, latency, and memory. The results suggest that diffusion LLMs may offer advantages for efficient deployment due to more quantization-resilience.

Diffusion Large Language Models (dLLMs) have emerged as a promising alternative to autoregressive generation by enabling parallel token prediction. However, practical dLLM decoding still suffers from high inference latency, which limits deployment. In this work, we observe that a substantial part of this inefficiency comes from recurring redundancy in the decoding process, including spatial redundancy caused by confidence clusters and positional ambiguity, and temporal redundancy caused by repeatedly remasking predictions that have already stabilized. Motivated by these patterns, we propose $R^{2}$-dLLM, a unified framework for reducing decoding redundancy from both inference and training perspectives. At inference time, we introduce training-free decoding rules that aggregate local confidence and token predictions, and finalize temporally stable tokens to avoid redundant decoding steps. We further propose a redundancy-aware supervised fine-tuning pipeline that aligns the model with efficient decoding trajectories and reduces reliance on manually tuned thresholds. Experiments demonstrate that $R^{2}$-dLLM consistently reduces the number of decoding steps by up to 88% compared to existing decoding strategies, while maintaining competitive generation quality across different models and tasks. These results validate that decoding redundancy is a central bottleneck in dLLMs, and that explicitly reducing it yields substantial practical efficiency gains. Our code and models are available at https://github.com/GATECH-EIC/R2-dLLM.