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Diffusion-based generative models represent the current state-of-the-art forimage generation. However, standard diffusion models are based on Euclideangeometry and do not translate directly to manifold-valued data. In this work,we develop extensions of both score-based generative models (SGMs) andDenoising Diffusion Probabilistic Models (DDPMs) to the Lie group of 3Drotations, SO(3). SO(3) is of particular interest in many disciplines such asrobotics, biochemistry and astronomy/cosmology science. Contrary to moregeneral Riemannian manifolds, SO(3) admits a tractable solution to heatdiffusion, and allows us to implement efficient training of diffusion models.We apply both SO(3) DDPMs and SGMs to synthetic densities on SO(3) anddemonstrate state-of-the-art results. Additionally, we demonstrate thepracticality of our model on pose estimation tasks and in predicting correlatedgalaxy orientations for astrophysics/cosmology.

Unified framework for diffusion generative models in SO(3): applications in computer vision and astrophysics