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