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On Diffusion Process in SE(3)-invariant Space
March 5, 2024, 2:42 p.m. | Zihan Zhou, Ruiying Liu, Jiachen Zheng, Xiaoxue Wang, Tianshu Yu
cs.LG updates on arXiv.org arxiv.org
Abstract: Sampling viable 3D structures (e.g., molecules and point clouds) with SE(3)-invariance using diffusion-based models proved promising in a variety of real-world applications, wherein SE(3)-invariant properties can be naturally characterized by the inter-point distance manifold. However, due to the non-trivial geometry, we still lack a comprehensive understanding of the diffusion mechanism within such SE(3)-invariant space. This study addresses this gap by mathematically delineating the diffusion mechanism under SE(3)-invariance, via zooming into the interaction behavior between coordinates …
abstract applications arxiv cs.lg diffusion geometry manifold molecules process sampling space type understanding world
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