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

arXiv: https://arxiv.org/abs/2508.04884 · HTML: https://mlsanity.com/paper/2508.04884/

## 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.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [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)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [The Diffusion Duality](https://mlsanity.com/paper/2506.10892/) (2025)
- [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021)
- [Align Your Steps: Optimizing Sampling Schedules in Diffusion Models](https://mlsanity.com/paper/2404.14507/) (2024)
- [textitJump Your Steps: Optimizing Sampling Schedule of Discrete Diffusion Models](https://mlsanity.com/paper/2410.07761/) (2024)
- [Score-Optimal Diffusion Schedules](https://mlsanity.com/paper/2412.07877/) (2024)
- [Provable benefits of annealing for estimating normalizing constants: Importance Sampling, Noise-Contrastive Estimation, and beyond](https://mlsanity.com/paper/2310.03902/) (2023)
- [Image generation with shortest path diffusion](https://mlsanity.com/paper/2306.00501/) (2023)
- [Using Ornstein-Uhlenbeck Process to understand Denoising Diffusion Probabilistic Model and its Noise Schedules](https://mlsanity.com/paper/2311.17673/) (2023)

## Built on by (most cited first, 11 of 11)

- [Error Bounds and Optimal Schedules for Masked Diffusions with Factorized Approximations](https://mlsanity.com/paper/2510.25544/) (2025)
- [Learning Boltzmann Generators via Constrained Mass Transport](https://mlsanity.com/paper/2510.18460/) (2025)
- [Learnable Sampler Distillation for Discrete Diffusion Models](https://mlsanity.com/paper/2509.19962/) (2025)
- [On the Design of One-step Diffusion via Shortcutting Flow Paths](https://mlsanity.com/paper/2512.11831/) (2025)
- [Discrete-WAM: Unified Discrete Vision-Action Token Editing for World-Policy Learning](https://mlsanity.com/paper/2606.05645/) (2026)
- [Accelerating Discrete Diffusion Models with Parallel-In-Time Sampling](https://mlsanity.com/paper/2607.00773/) (2026)
- [AnCoder: Anchored Code Generation via Discrete Diffusion Models](https://mlsanity.com/paper/2602.17688/) (2026)
- [Kinetic-Optimal Scheduling with Moment Correction for Metric-Induced Discrete Flow Matching in Zero-Shot Text-to-Speech](https://mlsanity.com/paper/2605.09386/) (2026)
- [A Gaussian Perspective for Distributional Discrepancy in Generative Diffusion Models](https://mlsanity.com/paper/2601.13602/) (2026)
- [The Loss Floor of Denoising Score Matching: Fisher Geometry from Schr"odinger Bridges](https://mlsanity.com/paper/2608.23916/) (2026)
- [Schedule optimization for tau-leaping in masked discrete diffusion](https://mlsanity.com/paper/2609.21960/) (2026)

## 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.