# Why Masking Diffusion Works: Condition on the Jump Schedule for Improved Discrete Diffusion

arXiv: https://arxiv.org/abs/2506.08316 · HTML: https://mlsanity.com/paper/2506.08316/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 20 of its 27 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 20 of 20)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [PixelSNAIL: An Improved Autoregressive Generative Model](https://mlsanity.com/paper/1712.09763/) (2017)
- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [Diffusion Language Models Are Versatile Protein Learners](https://mlsanity.com/paper/2402.18567/) (2024)
- [Path Planning for Masked Diffusion Model Sampling](https://mlsanity.com/paper/2502.03540/) (2025)
- [Think While You Generate: Discrete Diffusion with Planned Denoising](https://mlsanity.com/paper/2410.06264/) (2024)
- [Informed Correctors for Discrete Diffusion Models](https://mlsanity.com/paper/2407.21243/) (2024)
- [Learning-Order Autoregressive Models with Application to Molecular Graph Generation](https://mlsanity.com/paper/2503.05979/) (2025)

## Built on by (most cited first, 15 of 15)

- [Diffusion Language Models are Super Data Learners](https://mlsanity.com/paper/2511.03276/) (2025)
- [Scaling Behavior of Discrete Diffusion Language Models](https://mlsanity.com/paper/2512.10858/) (2025)
- [Coevolutionary Continuous Discrete Diffusion: Make Your Diffusion Language Model a Latent Reasoner](https://mlsanity.com/paper/2510.03206/) (2025)
- [Training Optimal Large Diffusion Language Models](https://mlsanity.com/paper/2510.03280/) (2025)
- [A Diffusion Model to Shrink Proteins While Maintaining Their Function](https://mlsanity.com/paper/2511.07390/) (2025)
- [Masked Diffusion Models are Secretly Learned-Order Autoregressive Models](https://mlsanity.com/paper/2511.19152/) (2025)
- [Generalized Discrete Diffusion from Snapshots](https://mlsanity.com/paper/2603.21342/) (2026)
- [Forward-Free Diffusion Language Models with BPTT-Free Looped Refinement](https://mlsanity.com/paper/2606.08357/) (2026)
- [A Unification of Discrete, Gaussian, and Simplicial Diffusion](https://mlsanity.com/paper/2512.15923/) (2025)
- [Manifold Aware Denoising Score Matching (MAD)](https://mlsanity.com/paper/2603.02452/) (2026)
- [Accelerating Masked Diffusion Large Language Models: A Survey of Efficient Inference Techniques](https://mlsanity.com/paper/2607.12829/) (2026)
- [Stratified Hazard Sampling: Minimal-Variance Event Scheduling for CTMC/DTMC Discrete Diffusion and Flow Models](https://mlsanity.com/paper/2601.02799/) (2026)
- [On the Error-Correcting Effects of Stochasticity in Discrete Diffusion](https://mlsanity.com/paper/2605.26582/) (2026)
- [Does Uniform Discrete Diffusion Need Time?](https://mlsanity.com/paper/2609.30977/) (2026)
- [Deep Generative Models for Phylogenetic Inference with Complex Evolutionary Processes](https://mlsanity.com/paper/2610.19053/) (2026)

## Abstract (arXiv)

Discrete diffusion models, like continuous diffusion models, generate high-quality samples by gradually undoing noise applied to datapoints with a Markov process. Gradual generation in theory comes with many conceptual benefits; for example, inductive biases can be incorporated into the noising Markov process, and access to improved sampling algorithms. In practice, however, the consistently best performing discrete diffusion model is, surprisingly, masking diffusion, which does not denoise gradually. Here we explain the superior performance of masking diffusion by noting that it makes use of a fundamental difference between continuous and discrete Markov processes: discrete Markov processes evolve by discontinuous jumps at a fixed rate and, unlike other discrete diffusion models, masking diffusion builds in the known distribution of jump times and only learns where to jump to. We show that we can similarly bake in the known distribution of jump times into any discrete diffusion model. The resulting models - schedule-conditioned discrete diffusion (SCUD) - generalize classical discrete diffusion and masking diffusion. By applying SCUD to models with noising processes that incorporate inductive biases on images, text, and protein data, we build models that outperform masking.