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

Leach, Adam; Schmon, Sebastian M.; Degiacomi, Matteo T.; Willcocks, Chris G.

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

Leach, Adam; Schmon, Sebastian M.; Degiacomi, Matteo T.; Willcocks, Chris G.

Authors

Adam Leach adam.leach@durham.ac.uk
PGR Student Doctor of Philosophy

Sebastian M. Schmon

Dr Matteo Degiacomi matteo.t.degiacomi@durham.ac.uk
Associate Professor

Dr Chris Willcocks christopher.g.willcocks@durham.ac.uk
Associate Professor

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 Rn. 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 na¨ıve approaches such as Euler angle diffusion in synthetic rotational distribution sampling and in a 3D object alignment task.

Citation

Leach, A., Schmon, S. M., Degiacomi, M. T., & Willcocks, C. G. (2022). Denoising Diffusion Probabilistic Models on SO(3) for Rotational Alignment.

Conference Name	ICLR 2022 Workshop on Geometrical and Topological Representation Learning
Start Date	Apr 29, 2022
Acceptance Date	Mar 25, 2022
Publication Date	2022
Deposit Date	Jun 24, 2022
Publicly Available Date	Jun 24, 2022
Publisher URL	https://gt-rl.github.io/papers