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.

翻译：扩散模型已成功应用于多种连续域的生成任务中。然而，将扩散应用于离散类别数据仍是一项具有挑战性的任务。此外，连续域中的生成过程在实际应用中往往需要引入裁剪操作，这促使我们需要为约束域中的扩散适配建立理论框架。受约束采样问题中镜像朗之万算法的启发，本理论报告提出了镜像扩散模型。我们在单纯形扩散的背景下对镜像扩散模型进行论证，并提出了向图像生成和文本生成等主流领域的自然扩展方案。