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

02 Mar 2022, 12:21 (modified: 25 Apr 2022, 15:26)GTRL 2022 PosterReaders: Everyone
Keywords: Diffusion Models, DDPM, Denoising Diffusion Probabilistic Models, Manifolds, Rotation, SO(3), Generative Model, Alignment, Probabilistic diffusion models, Data Distribution, Rotation, SO(3), Manifold Diffusion, Roto-translational alignment, Probabilistic Sampling
TL;DR: We make DDPMs work for rotations using distributions defined on SO(3), then use them for rotational alignment tasks.
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.
Poster: png