# Discrete Diffusion Models are Minimax Optimal Under Sparsity

arXiv: https://arxiv.org/abs/2610.19020 · HTML: https://mlsanity.com/paper/2610.19020/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 11 of its 19 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Placed in

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

## Builds on (most cited first, 11 of 11)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (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)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data](https://mlsanity.com/paper/2302.07194/) (2023)
- [Diffusion Models are Minimax Optimal Distribution Estimators](https://mlsanity.com/paper/2303.01861/) (2023)
- [Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions](https://mlsanity.com/paper/2409.18804/) (2024)
- [Discrete State Diffusion Models: A Sample Complexity Perspective](https://mlsanity.com/paper/2510.10854/) (2025)
- [Estimation of discrete distributions in relative entropy, and the deviations of the missing mass](https://mlsanity.com/paper/2504.21787/) (2025)
- [Minimax Optimality of Score-Entropy Discrete Diffusion](https://mlsanity.com/paper/2608.20635/) (2026)

## Abstract (arXiv)

Discrete diffusion models have emerged as a leading alternative to autoregressive models for generating text and other categorical data, yet their theoretical foundations remain less developed than those of their continuous counterparts. For continuous diffusion models, a prominent line of theory suggests that these models can adapt to low-dimensional structure in the data, thereby improving statistical efficiency and generalization. In this work, we investigate the discrete analogue of this phenomenon by studying the statistical rates of discrete diffusion models under sparsity assumptions. By analyzing a nonparametric estimator derived from a regularized score-entropy objective, we establish minimax-optimal rates in the sparse regime. The proposed regularization can be viewed as an adaptation of label smoothing techniques introduced for classification, and does not require the knowledge of the sparsity parameter. This shows that discrete diffusion models can adapt intrinsically to sparsity.