Masked diffusion models have emerged as a powerful framework for text and multimodal generation. However, their sampling procedure updates multiple tokens simultaneously and treats generated tokens as immutable, which may lead to error accumulation when early mistakes cannot be revised. In this work, we revisit existing self-correction methods and identify limitations stemming from additional training requirements or reliance on misaligned likelihood estimates. We propose a training-free self-correction framework that exploits the inductive biases of pre-trained masked diffusion models. Without modifying model parameters or introducing auxiliary evaluators, our method significantly improves generation quality on text-to-image generation and multimodal understanding tasks with reduced sampling steps. Moreover, the proposed framework generalizes across different masked diffusion architectures, highlighting its robustness and practical applicability. Code can be found in https://github.com/huge123/FreeCorrection.

Masked Diffusion Models (MDMs) have emerged as one of the most promising paradigms for generative modeling over discrete domains. It is known that MDMs effectively train to decode tokens in a random order, and that this ordering has significant performance implications in practice. This observation raises a fundamental question: can we design a training framework that optimizes for a favorable decoding order? We answer this in the affirmative, showing that the continuous-time variational objective of MDMs, when equipped with multivariate noise schedules, can identify and optimize for a decoding order during training. We establish a direct correspondence between decoding order and the multivariate noise schedule and show that this setting breaks invariance of the MDM objective to the noise schedule. Furthermore, we prove that the MDM objective decomposes precisely into a weighted auto-regressive losses over these orders, which establishes them as auto-regressive models with learnable orders.

Masked diffusion models (MDMs) offer a compelling alternative to autoregressive models (ARMs) for discrete text generation because they enable parallel token sampling, rather than sequential, left-to-right generation. This means potentially much faster inference. However, effective parallel sampling faces two competing requirements: (i) simultaneously updated tokens must be conditionally independent, and (ii) updates should prioritise high-confidence predictions. These goals conflict because high-confidence predictions often cluster and depend on each other, opportunities for parallel updates. We present PUNT, a model-agnostic sampler that reconciles this trade-off. Our method identifies token dependencies and removes lower-confidence tokens from conflicting groups. This produces sets of indices for unmasking that satisfy both independence and confidence criteria. Our approach ensures improved parallel unmasking through approximate conditional independence testing. Our experiments show that PUNT delivers a superior trade-off between accuracy and compute when compared to other strong training-free baselines, especially for generation of longer sequences. On the IFEval benchmark, it achieves up to 16\% higher accuracy over baseline methods, including sequential generation (one-by-one). These gains hold across different values of hyperparameters, mitigating the need for brittle hyperparameter tuning. Moreover, we observe that PUNT induces an emergent hierarchical generation strategy, where the model first establishes high-level paragraph structure before local refinement, suggesting a planning-like generation process that contributes to strong alignment performance.

Diffusion Transformer (DiT) is emerging as a cutting-edge trend in the landscape of generative diffusion models for image generation. Recently, masked-reconstruction strategies have been considered to improve the efficiency and semantic consistency in training DiT but suffer from deficiency in contextual information extraction. In this paper, we provide a new insight to reveal that noisy-to-noisy masked-reconstruction harms sufficient utilization of contextual information. We further demonstrate the insight with theoretical analysis and empirical study on the mutual information between unmasked and masked patches. Guided by such insight, we propose a novel training paradigm named MC-DiT for fully learning contextual information via diffusion denoising at different noise variances with clean-to-clean mask-reconstruction.

Masked Diffusion Models (MDMs) have emerged as a powerful generative modeling technique. Despite their remarkable results, they typically suffer from slow inference with several steps. In this paper, we propose Di$\mathtt{[M]}$O, a novel approach that distills masked diffusion models into a one-step generator. Di$\mathtt{[M]}$O addresses two key challenges: (1) the intractability of using intermediate-step information for one-step generation, which we solve through token-level distribution matching that optimizes model output logits by an 'on-policy framework' with the help of an auxiliary model; and (2) the lack of entropy in the initial distribution, which we address through a token initialization strategy that injects randomness while maintaining similarity to teacher training distribution. We show Di$\mathtt{[M]}$O's effectiveness on both class-conditional and text-conditional image generation, impressively achieving performance competitive to multi-step teacher outputs while drastically reducing inference time. To our knowledge, we are the first to successfully achieve one-step distillation of masked diffusion models and the first to apply discrete distillation to text-to-image generation, opening new paths for efficient generative modeling.