Unified framework for diffusion generative models in SO(3): applications in computer vision and astrophysics
This work addresses a bottleneck for researchers in robotics, biochemistry, and astrophysics who need to generate or analyze data on the 3D rotation manifold.
The authors tackled the problem of applying diffusion generative models to manifold-valued data by extending both score-based generative models and Denoising Diffusion Probabilistic Models to the Lie group SO(3), achieving state-of-the-art results on synthetic densities and demonstrating practical applications in pose estimation and astrophysics.
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.