Masked Diffusion Models

Retrieval-Augmented Generation (RAG) improves factual grounding by incorporating external knowledge into language model generation. However, when retrieved context is noisy, unreliable, or inconsistent with the model's parametric knowledge, it introduces retrieval-prior conflicts that can degrade generation quality. While this problem has been studied in autoregressive language models, it remains largely unexplored in diffusion-based language models, where the iterative denoising process introduces unique challenges for integrating retrieved context. In this work, we propose Adaptive Retrieval-Augmented Masked Diffusion (ARAM), a training-free adaptive guidance framework for Masked Diffusion Models (MDMs) in RAG settings. ARAM dynamically calibrates the guidance scale during denoising according to the Signal-to-Noise Ratio (SNR) of the distributional shift induced by retrieved context. Intuitively, the model strengthens guidance when the retrieved context provides reliable corrective evidence and suppresses it when the contextual signal is noisy or non-supportive. Extensive experiments on multiple knowledge-intensive QA benchmarks show that ARAM improves overall QA performance over competitive RAG baselines.

Standard masked discrete diffusion models face limitations in reasoning tasks due to their inability to correct their own mistakes on the masking path. Since they rely on a fixed number of denoising steps, they are unable to adjust their computation to the complexity of a given problem. To address these limitations, we introduce a method based on learning a Markov transition kernel that is trained on its own outputs. This design enables tokens to be remasked, allowing the model to correct its previous mistakes. Furthermore, we do not need a fixed time schedule but use a trained stopping criterion. This allows for adaptation of the number of function evaluations to the difficulty of the reasoning problem. Our adaptation adds two lightweight prediction heads, enabling reuse and fine-tuning of existing pretrained models. On the Sudoku-Extreme dataset we clearly outperform other flow based methods with a validity of 95%. For the Countdown-4 we only need in average of 10 steps to solve almost 96% of them correctly, while many problems can be solved already in 2 steps.

Masked diffusion language models (MDLMs) have recently emerged as a new paradigm in language modeling, offering flexible generation dynamics and enabling efficient parallel decoding. However, existing decoding strategies for pre-trained MDLMs predominantly rely on token-level uncertainty criteria, while largely overlooking sequence-level information and inter-token dependencies. To address this limitation, we propose Dependency-Oriented Sampler (DOS), a training-free decoding strategy that leverages inter-token dependencies to inform token updates during generation. Specifically, DOS exploits attention matrices from transformer blocks to approximate inter-token dependencies, emphasizing information from unmasked tokens when updating masked positions. Empirical results demonstrate that DOS consistently achieves superior performance on both code generation and mathematical reasoning tasks. Moreover, DOS can be seamlessly integrated with existing parallel sampling methods, leading to improved generation efficiency without sacrificing generation quality.

We present Dynin-Omni, the first masked-diffusion-based omnimodal foundation model that unifies text, image, and speech understanding and generation, together with video understanding, within a single architecture. Unlike autoregressive unified models that serialize heterogeneous modalities, or compositional unified models that require orchestration with external modality-specific decoders, Dynin-Omni natively formulates omnimodal modeling as masked diffusion over a shared discrete token space, enabling iterative refinement under bidirectional context. Dynin-Omni adopts a multi-stage training strategy with model-merging-based modality expansion and omnimodal alignment. We evaluate Dynin-Omni across 19 multimodal benchmarks spanning language reasoning, image generation and editing, video understanding, and speech recognition and synthesis. Dynin-Omni achieves 87.6 on GSM8K, 1733.6 on MME-P, 61.4 on VideoMME, 0.87 on GenEval, and 2.1 WER on LibriSpeech test-clean, consistently outperforming existing open-source unified models while remaining competitive with strong modality-specific expert systems. These results demonstrate the potential of masked diffusion as a unified paradigm for any-to-any modeling, providing a flexible foundation for real-time omnimodal systems, unified cross-modal retrieval and generation, and embodied multimodal agents.

Vision-based motion capture solutions often struggle with occlusions, which result in the loss of critical joint information and hinder accurate 3D motion reconstruction. Other wearable alternatives also suffer from noisy or unstable data, often requiring extensive manual cleaning and correction to achieve reliable results. To address these challenges, we introduce the Masked Motion Diffusion Model (MMDM), a diffusion-based generative reconstruction framework that enhances incomplete or low-confidence motion data using partially available high-quality reconstructions within a Masked Autoencoder architecture. Central to our design is the Kinematic Attention Aggregation (KAA) mechanism, which enables efficient, deep, and iterative encoding of both joint-level and pose-level features, capturing structural and temporal motion patterns essential for task-specific reconstruction. We focus on learning context-adaptive motion priors, specialized structural and temporal features extracted by the same reusable architecture, where each learned prior emphasizes different aspects of motion dynamics and is specifically efficient for its corresponding task. This enables the architecture to adaptively specialize without altering its structure. Such versatility allows MMDM to efficiently learn motion priors tailored to scenarios such as motion refinement, completion, and in-betweening. Extensive evaluations on public benchmarks demonstrate that MMDM achieves strong performance across diverse masking strategies and task settings. The source code is available at https://github.com/jjkislele/MMDM.

While recent multimodal large language models (MLLMs) have made impressive strides, they predominantly employ a conventional autoregressive architecture as their backbone, leaving significant room to explore effective and efficient alternatives in architectural design. Concurrently, recent studies have successfully applied discrete diffusion models to various domains, such as visual understanding and image generation, revealing their considerable potential as a promising backbone for multimodal systems. Drawing inspiration from these pioneering studies, we introduce Omni-Diffusion, the first any-to-any multimodal language model built entirely on mask-based discrete diffusion models, which unifies understanding and generation across text, speech, and images. Omni-Diffusion employs a unified mask-based discrete diffusion model to directly capture the joint distribution over discrete multimodal tokens. This approach supports not only bimodal tasks but also more complex scenarios involving multiple modalities. On a diverse set of benchmarks, our method outperforms or performs on par with existing multimodal systems that process two or more modalities, highlighting the significant promise of diffusion models in powering the next generation of multimodal foundation models. Project webpage: https://omni-diffusion.github.io.

Diffusion LLMs have been proposed as an alternative to autoregressive LLMs. Curiously, they are especially capable if the generation length, i.e., the number of tokens the model has to output, is set to a much higher value than the correct answer length, and the model pads its answer with end-of-sequence (EoS) tokens. We hypothesize that off-the-shelf masked diffusion LLMs use the representations of EoS tokens as additional computing capacity, which enhances their performance. We experiment with the diffusion models LLaDA1.5, LLaDA2.0-mini, and Dream-v0 on three reasoning tasks: Addition, Entity Tracking, and Sudoku. In a controlled prompting experiment, we confirm that adding EoS tokens improves the LLMs' performance. To further verify whether their representations are used for hidden computations, we perform a causal intervention and transfer the hidden states of the EoS tokens between generations, which increases the models' relative likelihood of outputting the counterfactual answer. The behavioral experiments and the causal interventions indicate that fully bidirectional masked diffusion LLMs can indeed perform latent reasoning in the representations of EoS tokens. Furthermore, we find that these results generalize beyond toy tasks and that providing the model with additional EoS tokens also improves performance on GSM8K and two-hop reasoning.

While Masked Diffusion Language Models (MDLMs) relying on token masking and unmasking have shown promise in language modeling, their computational efficiency and generation flexibility remain constrained by the masking paradigm. In this paper, we propose Deletion-Insertion Diffusion language models (DID) that rigorously formulate token deletion and insertion as discrete diffusion processes, replacing the masking and unmasking processes in current MDLMs. DID improves training and inference efficiency by eliminating two major sources of computational overhead in MDLMs: the computations on non-informative 1) <MASK> tokens inherent to the paradigm, and 2) <PAD> tokens introduced in variable-length settings. Furthermore, DID offers greater flexibility by: 1) natively supporting variable-length sequences without requiring fixed-length padding, and 2) an intrinsic self-correction mechanism during generation due to insertion that dynamically adjusts token positions. To train DID, we design a score-based approach that assigns scores to token insertion operations and derive appropriate training objectives. The objectives involve subsequence counting problems, which we efficiently solve via a parallelized dynamic programming algorithm. Our experiments across fixed and variable-length settings demonstrate the advantage of DID over baselines of MDLMs and existing insertion-based LMs, in terms of modeling performance, sampling quality, and training/inference speed, without any hyperparameter tuning.

Masked Diffusion Models (MDMs) provide an efficient non-causal alternative to autoregressive generation but often struggle with token dependencies and semantic incoherence due to their reliance on discrete marginal distributions. We address these limitations by shifting the diffusion process into a continuous sentence-level semantic space. We propose CRoCoDiL (Continuous and Robust Conditioned Diffusion for Language), a unified fine-tuning approach that jointly trains an encoder-demasker architecture, grounding the MDM demasking in continuous latent representations. This leads to the formation of a novel autoencoder in which decoding is obtained by an MDM algorithm. Relying on the same framework, we introduce two unconditional text synthesis algorithms: Continuous-Then-Discrete (ConThenDisc), a hybrid-diffusion approach that first generates latent representations in continuous space and then decodes these to tokens via an MDM, and Continuous-Within-Discrete (ConWithinDisc), a multi-diffusion strategy that refines latent representations throughout the discrete sampling process. Experiments using LLaDA show that our methods achieve superior generation quality and more than 10x faster sampling speeds in an unconditional setting.

Early DNA foundation models adopted BERT-style training, achieving good performance on DNA understanding tasks but lacking generative capabilities. Recent autoregressive models enable DNA generation, but employ left-to-right causal modeling that is suboptimal for DNA where regulatory relationships are inherently bidirectional. We present D3LM (Discrete DNA Diffusion Language Model), which unifies bidirectional representation learning and DNA generation through masked diffusion. D3LM directly adopts the Nucleotide Transformer (NT) v2 architecture but reformulates the training objective as masked diffusion in discrete DNA space, enabling both bidirectional understanding and generation capabilities within a single model. Compared to NT v2 of the same size, D3LM achieves improved performance on understanding tasks. Notably, on regulatory element generation, D3LM achieves an SFID of 10.92, closely approaching real DNA sequences (7.85) and substantially outperforming the previous best result of 29.16 from autoregressive models. Our work suggests diffusion language models as a promising paradigm for unified DNA foundation models. We further present the first systematic study of masked diffusion models in the DNA domain, investigating practical design choices such as tokenization schemes and sampling strategies, thereby providing empirical insights and a solid foundation for future research. D3LM has been released at https://huggingface.co/collections/Hengchang-Liu/d3lm.

Reinforcement Learning with Verifiable Rewards (RLVR) successfully aligns autoregressive models in rigorous domains like mathematical reasoning and code generation. However, applying RLVR to Diffusion Large Language Models (dLLMs) is hindered by intractable sequence-level likelihoods, forcing existing methods to rely on unstable, high-variance approximations. We propose Sequence Likelihood-Free Policy Optimization (LFPO), an efficient framework that circumvents this bottleneck by formulating policy alignment as discrete velocity alignment. Inspired by continuous flow matching, LFPO eschews trajectory-level estimation and directly optimizes denoising logits via contrastive token-level updates, providing a stable, low-variance surrogate. Furthermore, predicting terminal solutions from intermediate states implicitly straightens the generation trajectory, enabling high-quality sampling with significantly fewer denoising iterations. Extensive experiments on reasoning and coding benchmarks demonstrate that LFPO matches or exceeds the accuracy of likelihood-based baselines while substantially accelerating inference.

Masked diffusion models (MDMs) generate text by iteratively selecting positions to unmask and then predicting tokens at those positions. Yet MDMs lack proper likelihood evaluation: the evidence lower bound (ELBO) is not only a loose bound on log-likelihood, but, as we show, is also computed under the training distribution rather than the test-time distribution. We resolve this within our DUEL framework, which unifies leading MDM sampling strategies that employ $\textit{deterministic}$ position selection. We prove that DUEL samplers admit $\textbf{exact likelihood computation under the test-time distribution}$ -- giving MDMs $\textit{proper}$ likelihood, and hence proper perplexity, for the first time. This proper perplexity is the natural analogue of autoregressive perplexity and lets us revisit key questions about MDMs. $\textbf{MDMs are substantially better than previously thought}$: the MDM-autoregressive perplexity gap shrinks by up to $32\%$ on in-domain data and $82\%$ on zero-shot benchmarks. DUEL enables the first principled comparison of fast,parallel samplers across compute budgets -- an analysis impossible with the ELBO and unreliable with generative perplexity -- identifying a strong default method. Finally, oracle search over position orderings reveals MDMs can far surpass autoregressive models -- achieving $36.47$ vs. $52.11$ perplexity on AG News -- demonstrating the ceiling of MDM performance has not yet been reached.

Unlike autoregressive models, which generate tokens sequentially and benefit from reasoning-before-answering strategies such as Chain-of-Thought, Masked Diffusion Language Models (MDLMs) refine all sequence positions simultaneously, raising questions about how these models handle tasks requiring justified verdicts. In this work, we investigate the dynamics of MDLM reasoning on fact verification, examining whether justifications serve as genuine reasoning or post-hoc rationalization. We observe that MDLMs typically converge on a verdict early in the diffusion process, treating it as a global anchor that is resolved before the justification is complete. Crucially, enforcing a reasoning-first constraint via delayed verdict unmasking actively degrades performance, dropping accuracy from 86.2% to 71.9% as accumulating justification tokens introduce inconsistencies that override initially correct predictions. Interventional experiments reveal that the model rationalizes incorrect forced verdicts in 56% of cases, and that verdicts are strongly causally dependent on justification quality (57.3% accuracy with corrupted justifications vs. 97.1% with ground-truth). This causal dependence explains the degradation under forced deliberation: as the model generates noisy justification tokens, it conditions on them, gradually overriding its initially correct assessment. Our findings suggest that for fact verification with MDLMs, extended deliberation can be counterproductive, risking the dilution of accurate early predictions with noise introduced during justification generation.

Masked discrete diffusion models (MDMs) are a promising new approach to generative modelling, offering the ability for parallel token generation and therefore greater efficiency than autoregressive counterparts. However, achieving an optimal balance between parallel generation and sample quality remains an open problem. Current approaches primarily address this issue through fixed, heuristic parallel sampling methods. There exist some recent learning based approaches to this problem, but its formulation from the perspective of variational inference remains underexplored. In this work, we propose a variational inference framework for learning parallel generation orders for MDMs. As part of our method, we propose a parameterisation for the approximate posterior of generation orders which facilitates parallelism and efficient sampling during training. Using this method, we conduct preliminary experiments on the GSM8K dataset, where our method performs competitively against heuristic sampling strategies in the regime of highly parallel generation. For example, our method achieves 33.1% accuracy with an average of only only 4 generation steps, compared to 23.7-29.0% accuracy achieved by standard competitor methods in the same number of steps. We believe further experiments and analysis of the method will yield valuable insights into the problem of parallel generation with MDMs.

Time series anomaly detection (TSAD) has been an important area of research for decades, with reconstruction-based methods, mostly based on generative models, gaining popularity and demonstrating success. Diffusion models have recently attracted attention due to their advanced generative capabilities. Existing diffusion-based methods for TSAD rely on a conditional strategy, which reconstructs input instances from white noise with the aid of the conditioner. However, this poses challenges in accurately reconstructing the normal parts, resulting in suboptimal detection performance. In response, we propose a novel diffusion-based method, named AnomalyFilter, which acts as a selective filter that only denoises anomaly parts in the instance while retaining normal parts. To build such a filter, we mask Gaussian noise during the training phase and conduct the denoising process without adding noise to the instances. The synergy of the two simple components greatly enhances the performance of naive diffusion models. Extensive experiments on five datasets demonstrate that AnomalyFilter achieves notably low reconstruction error on normal parts, providing empirical support for its effectiveness in anomaly detection. AnomalyFilter represents a pioneering approach that focuses on the noise design of diffusion models specifically tailored for TSAD.

Detection of rare lesions in whole-body CT is fundamentally limited by extreme class imbalance and low target-to-volume ratios, producing precision collapse despite high AUROC. Synthetic augmentation with diffusion models offers promise, yet pixel-space diffusion is computationally expensive, and existing mask-conditioned approaches lack controllable attribute-level regulation and paired supervision for accountable training. We introduce SALIENT, a mask-conditioned wavelet-domain diffusion framework that synthesizes paired lesion-masking volumes for controllable CT augmentation under long-tail regimes. Instead of denoising in pixel space, SALIENT performs structured diffusion over discrete wavelet coefficients, explicitly separating low-frequency brightness from high-frequency structural detail. Learnable frequency-aware objectives disentangle target and background attributes (structure, contrast, edge fidelity), enabling interpretable and stable optimization. A 3D VAE generates diverse volumetric lesion masks, and a semi-supervised teacher produces paired slice-level pseudo-labels for downstream mask-guided detection. SALIENT improves generative realism, as reflected by higher MS-SSIM (0.63 to 0.83) and lower FID (118.4 to 46.5). In a separate downstream evaluation, SALIENT-augmented training improves long-tail detection performance, yielding disproportionate AUPRC gains across low prevalences and target-to-volume ratios. Optimal synthetic ratios shift from 2x to 4x as labeled seed size decreases, indicating a seed-dependent augmentation regime under low-label conditions. SALIENT demonstrates that frequency-aware diffusion enables controllable, computationally efficient precision rescue in long-tail CT detection.

Discrete diffusion models have achieved strong empirical performance in text and other symbolic domains, with masked (absorbing-rate) variants emerging as competitive alternatives to autoregressive models. Among existing samplers, the Euler method remains the standard choice in many applications, and more recently, the First-Hitting Sampler (FHS) has shown considerable promise for masked diffusion models. Despite their practical success, the theoretical understanding of these samplers remains limited. Existing analyses are conducted in Kullback-Leibler (KL) divergence, which often yields loose parameter dependencies and requires strong assumptions on score estimation. Moreover, these guarantees do not cover recently developed high-performance sampler of FHS. In this work, we first develop a direct total-variation (TV) based analysis for the Euler method that overcomes these limitations. Our results relax assumptions on score estimation, improve parameter dependencies, and establish convergence guarantees without requiring any surrogate initialization. Also for this setting, we provide the first convergence lower bound for the Euler sampler, establishing tightness with respect to both the data dimension $d$ and the target accuracy $\varepsilon$. Finally, we analyze the FHS sampler and show that it incurs no sampling error beyond that induced by score estimation, which we show to be tight with a matching lower error bound. Overall, our analysis introduces a direct TV-based error decomposition along the CTMC trajectory and a decoupling-based path-wise analysis for FHS, which may be of independent interest.

Discrete diffusion models have emerged as strong alternatives to autoregressive language models, with recent work initializing and fine-tuning a base unimodal model for bimodal generation. Diverging from previous approaches, we introduce the first tri-modal masked diffusion model pretrained from scratch on text, image-text, and audio-text data. We systematically analyze multimodal scaling laws, modality mixing ratios, noise schedules, and batch-size effects, and we provide optimized inference sampling defaults. Our batch-size analysis yields a novel stochastic differential equation (SDE)-based reparameterization that eliminates the need for tuning the optimal batch size as reported in recent work. This reparameterization decouples the physical batch size, often chosen based on compute constraints (GPU saturation, FLOP efficiency, wall-clock time), from the logical batch size, chosen to balance gradient variance during stochastic optimization. Finally, we pretrain a preliminary 3B-parameter tri-modal model on 6.4T tokens, demonstrating the capabilities of a unified design and achieving strong results in text generation, text-to-image tasks, and text-to-speech tasks. Our work represents the largest-scale systematic open study of multimodal discrete diffusion models conducted to date, providing insights into scaling behaviors across multiple modalities.

Visual counterfactual explanations aim to reveal the minimal semantic modifications that can alter a model's prediction, providing causal and interpretable insights into deep neural networks. However, existing diffusion-based counterfactual generation methods are often computationally expensive, slow to sample, and imprecise in localizing the modified regions. To address these limitations, we propose MaskDiME, a simple, fast, yet effective diffusion framework that unifies semantic consistency and spatial precision through localized sampling. Our approach adaptively focuses on decision-relevant regions to achieve localized and semantically consistent counterfactual generation while preserving high image fidelity. Our training-free framework, MaskDiME, performs inference over 30x faster than the baseline and achieves comparable or state-of-the-art performance across five benchmark datasets spanning diverse visual domains, establishing a practical and generalizable solution for efficient counterfactual explanation.

Existing insertion-based masked diffusion models that generate sequences by interleaving token insertion with unmasking use fixed schedules that are not dependent on the data. For structured sequences like graphs and molecules, learning data-dependent generation orders can improve generation quality by reducing uncertainty over the action space. We propose LoFlexMDM, an insertion-based masked diffusion model with learnable order dynamics that learns data-dependent insertion and unmasking rates. We generalize the discrete flow matching framework to work with variable-length sequences, propose a tractable schedule parameterization and a training objective for joint training of the generator and the target order dynamics. On De Novo and fragment-constrained molecule generation, LoFlexMDM improves sample quality over FlexMDM by up to 17.5% and 6.7%, respectively. These results show that learning the target generation order can improve insertion-based diffusion models without giving up tractable training. We open source the code at https://github.com/dhruvdcoder/LoFlexMDM.

Masked Diffusion Models (MDMs) enable flexible decoding orders, yet existing samplers remain largely greedy, selecting locally certain tokens without accounting for their downstream effects. We show that this myopia can increase cumulative uncertainty and lead to suboptimal generation. To address this, we propose the Info-Gain Sampler, a training-free decoding method that uses the bidirectional structure of MDMs to balance immediate uncertainty with the information gained over remaining masked positions. Across reasoning, coding, creative writing, and image generation tasks, Info-Gain Sampler consistently outperforms existing MDM samplers, improving average reasoning accuracy by 2.9--11.6 percentage points and achieving a 62.8% average win rate in creative writing. The code is available at https://github.com/yks23/Information-Gain-Sampler.

Physical fields are typically observed only at sparse, time-varying sensor locations, making forecasting and reconstruction ill-posed and uncertainty-critical. We present SOLID, a mask-conditioned diffusion framework that learns spatiotemporal dynamics from sparse observations alone: training and evaluation use only observed target locations, requiring no dense fields and no pre-imputation. Unlike prior work that trains on dense reanalysis or simulations and only tests under sparsity, SOLID is trained end-to-end with sparse supervision only. SOLID conditions each denoising step on the measured values and their locations, and introduces a dual-masking objective that (i) emphasizes learning in unobserved void regions while (ii) upweights overlap pixels where inputs and targets provide the most reliable anchors. This strict sparse-conditioning pathway enables posterior sampling of full fields consistent with the measurements, achieving up to an order-of-magnitude improvement in probabilistic error and yielding calibrated uncertainty maps (\r{ho} > 0.7) under severe sparsity.

Diffusion language models are a promising alternative to autoregressive models due to their potential for faster generation. Among discrete diffusion approaches, Masked diffusion currently dominates, largely driven by strong perplexity on language modeling benchmarks. In this work, we present the first scaling law study of uniform-state and interpolating discrete diffusion methods. We also show that Masked diffusion models can be made approximately 12% more FLOPs-efficient when trained with a simple cross-entropy objective. We find that perplexity is informative within a diffusion family but can be misleading across families, where models with worse likelihood scaling may be preferable due to faster and more practical sampling, as reflected by the speed-quality Pareto frontier. These results challenge the view that Masked diffusion is categorically the future of diffusion language modeling and that perplexity alone suffices for cross-algorithm comparison. Scaling all methods to 1.7B parameters, we show that uniform-state diffusion remains competitive on likelihood-based benchmarks and outperforms autoregressive and Masked diffusion models on GSM8K, despite worse validation perplexity. We provide the code, model checkpoints, and video tutorials on the project page: http://s-sahoo.github.io/scaling-dllms

Vision-Language-Action (VLA) models for autonomous driving increasingly adopt generative planners trained with imitation learning followed by reinforcement learning. Diffusion-based planners suffer from modality alignment difficulties, low training efficiency, and limited generalization. Token-based planners are plagued by cumulative causal errors and irreversible decoding. In summary, the two dominant paradigms exhibit complementary strengths and weaknesses. In this paper, we propose DriveFine, a masked diffusion VLA model that combines flexible decoding with self-correction capabilities. In particular, we design a novel plug-and-play block-MoE, which seamlessly injects a refinement expert on top of the generation expert. By enabling explicit expert selection during inference and gradient blocking during training, the two experts are fully decoupled, preserving the foundational capabilities and generic patterns of the pretrained weights, which highlights the flexibility and extensibility of the block-MoE design. Furthermore, we design a hybrid reinforcement learning strategy that encourages effective exploration of refinement expert while maintaining training stability. Extensive experiments on NAVSIM v1, v2, and Navhard benchmarks demonstrate that DriveFine exhibits strong efficacy and robustness. The code will be released at https://github.com/MSunDYY/DriveFine.

Masked diffusion models (MDMs) have emerged as a promising alternative to autoregressive models, enabling parallel token generation while achieving competitive performance. Despite these advantages, MDMs face a fundamental limitation: once tokens are unmasked, they remain fixed, leading to error accumulation and ultimately degrading sample quality. We address this by proposing a framework that trains a model to perform both unmasking and correction. By reusing outputs from the MDM denoising network as inputs for corrector training, we train a model to recover from potential mistakes. During generation we apply additional corrective refinement steps between unmasking ones in order to change decoded tokens and improve outputs. We name our training and sampling method Progressive Self-Correction (ProSeCo) for its unique ability to iteratively refine an entire sequence, including already generated tokens. We conduct extensive experimental validation across multiple conditional and unconditional tasks, demonstrating that ProSeCo yields better quality-efficiency trade-offs (up to ~4x faster sampling while still outperforming the best accuracy baseline method) and enables further gains through inference-time compute scaling (up to ~1.2x improvement on benchmarks when allowing for slower, high-NFE decoding).

Autoregressive language models (ARMs) suffer from the reversal curse: after learning ''$A$ is $B$,'' they often fail on the reverse query ''$B$ is $A$.'' Masked diffusion language models (MDMs) exhibit this failure in a much weaker form, but the underlying reason has remained unclear. A common explanation attributes this mitigation to their any-order masked training objective. However, observing ''$[\mathbf{M}]$ is $B$'' during training teaches recovery of $A$ from $B$ in one positional configuration, and does not by itself explain why the learned evidence should transfer to the reverse prompt ''$B$ is $[\mathbf{M}]$.'' We provide a theoretical analysis showing that this transfer arises from a parameter-level coupling between forward and reverse positional conditionals: shared Transformer parameters store token-pair evidence, while relative positional encodings route attention through queries and keys without changing the value-side evidence being retrieved. In a one-layer MDM, we prove that forward masked training strengthens evidence that is reusable in reverse queries, induces correlated forward--reverse attention routes, and yields a positively aligned shared-storage gradient component that decreases the reverse loss to first order. Controlled one-layer experiments and large-scale LLaDA/Dream experiments verify these signatures and show that they translate into improved reverse prediction.

Discrete Diffusion Language Models (DLMs) offer a promising non-autoregressive alternative for text generation, yet effective mechanisms for inference-time control remain relatively underexplored. Existing approaches include sampling-level guidance or trajectory optimization mechanisms. In this work, we study the paradigm of reference-based latent steering for DLMs. We introduce Iterative Latent Representation Refinement (ILRR), an efficient framework for steering DLMs using a reference text as a high-level semantic blueprint. ILRR extracts and injects reference-derived semantic signals into the evolving activations of the generated sequence, enabling tunable transfer of coarse properties such as sentiment. We further introduce Spatially Modulated Steering, an extension that enables long-form generation to be guided by shorter references by regulating intensity across the sequence. Empirically, we demonstrate that ILRR achieves effective control on LLaDA and MDLM architectures with low computational overhead, requiring only one additional parallel forward pass per denoising step. Under comparable compute budgets, ILRR improves attribute accuracy over baselines by 10% to 60% points. Our results suggest that the iterative, global denoising process makes DLMs a natural substrate for effective sequence-wide activation-level control.

Post-training pretrained autoregressive models (ARMs) into masked diffusion models (MDMs) provides an efficient route to diffusion language modeling, but it remains unclear whether the resulting models reuse inherited autoregressive computation or reorganize it for non-autoregressive generation. We compare two 7B ARM-MDM families across four controlled diagnostic tasks and find a task-dependent mechanism shift. On prefix-dominant tasks, MDMs largely preserve inherited high-attribution pathways or exhibit only modest changes in where computation occurs. On globally constrained tasks, the reorganization is substantially stronger, with task-relevant computation shifting toward earlier layers. This depth-wise pattern persists across prompt resampling, circuit budgets, and tested inference budgets, while targeted ablations support the functional importance of the identified structures under the tested intervention protocols. At the component level, diagnostic probes suggest that ARMs rely more strongly on sharply specialized components, whereas MDMs exhibit weaker single-component specialization and more diffuse output-space alignment. Together, these results suggest that diffusion post-training selectively preserves or reorganizes inherited computation according to task structure, rather than uniformly replacing autoregressive mechanisms.

Masked Discrete Diffusion Models (MDMs) have achieved strong performance across a wide range of multimodal tasks, including image understanding, generation, and editing. However, their inference speed remains suboptimal due to the need to repeatedly process redundant masked tokens at every sampling step. In this work, we propose Sparse-LaViDa, a novel modeling framework that dynamically truncates unnecessary masked tokens at each inference step to accelerate MDM sampling. To preserve generation quality, we introduce specialized register tokens that serve as compact representations for the truncated tokens. Furthermore, to ensure consistency between training and inference, we design a specialized attention mask that faithfully matches the truncated sampling procedure during training. Built upon the state-of-the-art unified MDM LaViDa-O, Sparse-LaViDa achieves up to a 2x speedup across diverse tasks including text-to-image generation, image editing, and mathematical reasoning, while maintaining generation quality.

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