Denoising Diffusion Probabilistic Models on SO(3) for Rotational AlignmentDownload PDF

Published: 25 Mar 2022, Last Modified: 05 May 2023GTRL 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.
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