mlsanityData to 14 Oct 2026

The Cosine Schedule is Fisher-Rao-Optimal for Masked Discrete Diffusion Models

arXiv 2508.04884 ↗First posted 6 Aug 2025stat.ML cs.LGcited by 11

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

In this work, we study the problem of choosing the discretisation schedule for sampling from masked discrete diffusion models in terms of the information geometry of the induced probability path. Specifically, we show that the optimal schedule under the Fisher-Rao geometry recovers the popularly-used cosine schedule.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 17 of its 24 references that are in the map. First posted on arXiv 6 Aug 2025.

Builds on

17 of 24 references.

Closest ancestors · 10

Same direction, newest first

  1. 2024Score-Optimal Diffusion Schedules10 Dec
  2. 2024textitJump Your Steps: Optimizing Sampling Schedule of Discrete Diffusion Models10 Oct
  3. 2024Align Your Steps: Optimizing Sampling Schedules in Diffusion Models22 Apr
  4. 2023Using Ornstein-Uhlenbeck Process to understand Denoising Diffusion Probabilistic Model and its Noise Schedules29 Nov
  5. 2023Image generation with shortest path diffusion1 Jun
  6. 2022A Continuous Time Framework for Discrete Denoising Models30 May
  7. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  8. 2021Learning to Efficiently Sample from Diffusion Probabilistic Models7 Jun
  9. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov

Other references · 7

  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  3. 2024Simple and Effective Masked Diffusion Language Modelscited by 848
  4. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 626
  5. 2025Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusionscited by 214
  6. 2025The Diffusion Dualitycited by 135
  7. 2023Provable benefits of annealing for estimating normalizing constants: Importance Sampling, Noise-Contrastive Estimation, and beyondcited by 13

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 7.

11 papers.

  1. 2025Error Bounds and Optimal Schedules for Masked Diffusions with Factorized Approximationscited by 14
  2. 2025Learning Boltzmann Generators via Constrained Mass Transportcited by 9
  3. 2025Learnable Sampler Distillation for Discrete Diffusion Modelscited by 8
  4. 2025On the Design of One-step Diffusion via Shortcutting Flow Pathscited by 4
  5. 2026Discrete-WAM: Unified Discrete Vision-Action Token Editing for World-Policy Learningcited by 4
  6. 2026Accelerating Discrete Diffusion Models with Parallel-In-Time Samplingcited by 4
  7. 2026AnCoder: Anchored Code Generation via Discrete Diffusion Modelscited by 1
  8. 2026Kinetic-Optimal Scheduling with Moment Correction for Metric-Induced Discrete Flow Matching in Zero-Shot Text-to-Speechcited by 1
  9. 2026A Gaussian Perspective for Distributional Discrepancy in Generative Diffusion Modelscited by 0
  10. 2026The Loss Floor of Denoising Score Matching: Fisher Geometry from Schr"odinger Bridgescited by 0
  11. 2026Schedule optimization for tau-leaping in masked discrete diffusioncited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Why Masking Diffusion Works: Condition on the Jump Schedule for Improved Discrete Diffusion
  2. 2026The data geometry of masking diffusion: Certified-optimal schedules via unmasking growth complexity
  3. 2026Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees
  4. 2025Masked Diffusion Models as Energy Minimization
  5. 2025Masked Diffusion Models are Secretly Learned-Order Autoregressive Models
  6. 2026Noise Schedule Design for Diffusion Models: An Optimal Control Perspective
  7. 2025Path Planning for Masked Diffusion Model Sampling
  8. 2025Optimal Inference Schedules for Masked Diffusion Models