On Diffusion Process in SE(3)-invariant Space
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 no...
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Main Authors | , , , , |
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Format | Journal Article |
Language | English |
Published |
03.03.2024
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Subjects | |
Online Access | Get full text |
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Summary: | 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
and the inter-point distance manifold through the lens of differential
geometry. Upon this analysis, we propose accurate and projection-free diffusion
SDE and ODE accordingly. Such formulations enable enhancing the performance and
the speed of generation pathways; meanwhile offering valuable insights into
other systems incorporating SE(3)-invariance. |
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DOI: | 10.48550/arxiv.2403.01430 |