Methods based on Denoising Diffusion Probabilistic Models (DDPM) became a ubiquitous tool in generative modeling. However, they are mostly limited to Gaussian and discrete diffusion processes. We propose Star-Shaped Denoising Diffusion Probabilistic Models (SS-DDPM), a model with a non-Markovian diffusion-like noising process. In the case of Gaussian distributions, this model is equivalent to Markovian DDPMs. However, it can be defined and applied with arbitrary noising distributions, and admits efficient training and sampling algorithms for a wide range of distributions that lie in the exponential family. We provide a simple recipe for designing diffusion-like models with distributions like Beta, von Mises--Fisher, Dirichlet, Wishart and others, which can be especially useful when data lies on a constrained manifold such as the unit sphere, the space of positive semi-definite matrices, the probabilistic simplex, etc. 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.

翻译：基于去噪扩散概率模型（DDPM）的方法已成为生成建模中不可或缺的工具。然而，这类方法大多局限于高斯分布和离散扩散过程。我们提出星形去噪扩散概率模型（SS-DDPM），这是一种具有非马尔可夫类扩散加噪过程的模型。在高斯分布情形下，该模型等价于马尔可夫DDPM。但SS-DDPM可针对任意加噪分布进行定义和应用，并为指数族中广泛分布类型提供高效的训练与采样算法。我们提出一种简单配方，用于设计基于Beta分布、von Mises-Fisher分布、Dirichlet分布、Wishart分布等特定分布的类扩散模型，这类模型在数据位于约束流形（如单位球面、半正定矩阵空间、概率单纯形等）时尤为适用。我们在不同场景下评估该模型，发现其在图像数据上同样具有竞争力——基于Beta分布的SS-DDPM可取得与高斯DDPM相当的结果。