  AI-based molecule generation provides a promising approach to a large area of
biomedical sciences and engineering, such as antibody design, hydrolase
engineering, or vaccine development. Because the molecules are governed by
physical laws, a key challenge is to incorporate prior information into the
training procedure to generate high-quality and realistic molecules. We propose
a simple and novel approach to steer the training of diffusion-based generative
models with physical and statistics prior information. This is achieved by
constructing physically informed diffusion bridges, stochastic processes that
guarantee to yield a given observation at the fixed terminal time. We develop a
Lyapunov function based method to construct and determine bridges, and propose
a number of proposals of informative prior bridges for both high-quality
molecule generation and uniformity-promoted 3D point cloud generation. With
comprehensive experiments, we show that our method provides a powerful approach
to the 3D generation task, yielding molecule structures with better quality and
stability scores and more uniformly distributed point clouds of high qualities.
