# Mirror Diffusion Models

arXiv: https://arxiv.org/abs/2308.06342 · HTML: https://mlsanity.com/paper/2308.06342/

## 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 1 of its 22 references that are in the map.
- First posted on arXiv 11 Aug 2023.

## Placed in

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

## Builds on (most cited first, 1 of 1)

- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)

## Abstract (arXiv)

Diffusion models have successfully been applied to generative tasks in various continuous domains. However, applying diffusion to discrete categorical data remains a non-trivial task. Moreover, generation in continuous domains often requires clipping in practice, which motivates the need for a theoretical framework for adapting diffusion to constrained domains. Inspired by the mirror Langevin algorithm for the constrained sampling problem, in this theoretical report we propose Mirror Diffusion Models (MDMs). We demonstrate MDMs in the context of simplex diffusion and propose natural extensions to popular domains such as image and text generation.