Mirror Diffusion Models
This work addresses a theoretical gap in adapting diffusion models for constrained and discrete data, which is incremental as it builds on existing mirror Langevin algorithms.
The authors tackled the challenge of applying diffusion models to discrete categorical data and constrained domains by proposing Mirror Diffusion Models (MDMs), demonstrating them for simplex diffusion and extending to domains like image and text generation.
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.