Star-Shaped Denoising Diffusion Probabilistic Models

TL;DR

This paper introduces Star-Shaped DDPMs, a new class of diffusion models that can handle a variety of distributions beyond Gaussian, enabling generative modeling on constrained manifolds with competitive results.

Contribution

The paper proposes the SS-DDPM framework, allowing diffusion models to incorporate diverse distributions like Beta and Dirichlet, overcoming limitations of traditional Gaussian-based DDPMs.

Findings

SS-DDPM is equivalent to DDPM for Gaussian distributions.

Beta SS-DDPM achieves results comparable to Gaussian DDPM on image data.

The method enables diffusion modeling on constrained manifolds.

Abstract

Denoising Diffusion Probabilistic Models (DDPMs) provide the foundation for the recent breakthroughs in generative modeling. Their Markovian structure makes it difficult to define DDPMs with distributions other than Gaussian or discrete. In this paper, we introduce Star-Shaped DDPM (SS-DDPM). Its star-shaped diffusion process allows us to bypass the need to define the transition probabilities or compute posteriors. We establish duality between star-shaped and specific Markovian diffusions for the exponential family of distributions and derive efficient algorithms for training and sampling from SS-DDPMs. In the case of Gaussian distributions, SS-DDPM is equivalent to DDPM. However, SS-DDPMs provide a simple recipe for designing diffusion models with distributions such as Beta, von Mises$\unicode{x2013}$Fisher, Dirichlet, Wishart and others, which can be especially useful when data lies on a constrained manifold. We evaluate the model in different settings and find it competitive even on image data, where Beta SS-DDPM achieves results comparable to a Gaussian DDPM. Our implementation is available at https://github.com/andrey-okhotin/star-shaped .