Authors: Shengjie Luo, Yixian Xu, Di He, Shuxin Zheng, Tie-Yan Liu, Liwei Wang
Abstract: The accurate prediction of geometric state evolution in complex systems is
critical for advancing scientific domains such as quantum chemistry and
material modeling. Traditional experimental and computational methods face
challenges in terms of environmental constraints and computational demands,
while current deep learning approaches still fall short in terms of precision
and generality. In this work, we introduce the Geometric Diffusion Bridge
(GDB), a novel generative modeling framework that accurately bridges initial
and target geometric states. GDB leverages a probabilistic approach to evolve
geometric state distributions, employing an equivariant diffusion bridge
derived by a modified version of Doob’s $h$-transform for connecting geometric
states. This tailored diffusion process is anchored by initial and target
geometric states as fixed endpoints and governed by equivariant transition
kernels. Moreover, trajectory data can be seamlessly leveraged in our GDB
framework by using a chain of equivariant diffusion bridges, providing a more
detailed and accurate characterization of evolution dynamics. Theoretically, we
conduct a thorough examination to confirm our framework’s ability to preserve
joint distributions of geometric states and capability to completely model the
underlying dynamics inducing trajectory distributions with negligible error.
Experimental evaluations across various real-world scenarios show that GDB
surpasses existing state-of-the-art approaches, opening up a new pathway for
accurately bridging geometric states and tackling crucial scientific challenges
with improved accuracy and applicability.
Source: http://arxiv.org/abs/2410.24220v1
