Structure Preserving Diffusion Models

arXiv:2402.19369v1 Announce Type: new
Abstract: Diffusion models have become the leading distribution-learning method in recent years. Herein, we introduce structure-preserving diffusion processes, a family of diffusion processes for learning distributions that possess additional structure, such as group symmetries, by developing theoretical conditions under which the diffusion transition steps preserve said symmetry. While also enabling equivariant data sampling trajectories, we exemplify these results by developing a collection of different symmetry equivariant diffusion models capable of learning distributions that are inherently symmetric. …

abstract arxiv become cs.cv cs.lg data diffusion diffusion models distribution enabling family processes symmetry transition type