Unified framework for diffusion generative models in SO(3): applications
  in computer vision and astrophysics
Yesukhei Jagvaral Francois Lanusse Rachel Mandelbaum
Diffusion-based generative models represent the current state-of-the-art for
image generation. However, standard diffusion models are based on Euclidean
geometry and do not translate directly to manifold-valued data. In this work,
we develop extensions of both score-based generative models (SGMs) and
Denoising Diffusion Probabilistic Models (DDPMs) to the Lie group of 3D
rotations, SO(3). SO(3) is of particular interest in many disciplines such as
robotics, biochemistry and astronomy/cosmology science. Contrary to more
general Riemannian manifolds, SO(3) admits a tractable solution to heat
diffusion, and allows us to implement efficient training of diffusion models.
We apply both SO(3) DDPMs and SGMs to synthetic densities on SO(3) and
demonstrate state-of-the-art results. Additionally, we demonstrate the
practicality of our model on pose estimation tasks and in predicting correlated
galaxy orientations for astrophysics/cosmology.