On Diffusion Process in SE(3)-invariant Space
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910351033892864 |
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| author | Zhou, Zihan Liu, Ruiying Zheng, Jiachen Wang, Xiaoxue Yu, Tianshu |
| author_facet | Zhou, Zihan Liu, Ruiying Zheng, Jiachen Wang, Xiaoxue Yu, Tianshu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01430 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Diffusion Process in SE(3)-invariant Space Zhou, Zihan Liu, Ruiying Zheng, Jiachen Wang, Xiaoxue Yu, Tianshu Machine Learning 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. |
| title | On Diffusion Process in SE(3)-invariant Space |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2403.01430 |