Denoising Diffusion Probabilistic Models on SO(3) for Rotational Alignment

Abstract

Probabilistic diffusion models are capable of modeling complex data distributions on high-dimensional Euclidean spaces for a range applications. However, many real world tasks involve more complex structures such as data distributions defined on manifolds which cannot be easily represented by diffusions on $\mathbb{R}^n$. This paper proposes denoising diffusion models for tasks involving 3D rotations leveraging diffusion processes on the Lie group $SO(3)$ in order to generate candidate solutions to rotational alignment tasks. The experimental results show the proposed $SO(3)$ diffusion process outperforms naïve approaches such as Euler angle diffusion in synthetic rotational distribution sampling and in a 3D object alignment task.