The diffusion model gains more and more attention in scientific computing and molecular simulations. As the molecular potential generally involves rigid bond constraints, we are interested in performing the diffusion generation on manifolds, i.e., bypassing the fast degrees of freedom. We will present two approaches: Riemannian DDPM for the direct generation on manifolds, and NISO-DM and Tango-DM on Euclidean space by utilizing the singularity structure of score function. The proposed methods do not rely on the specific manifold structure, which is typically assumed in previous literature.
Dr. Tiejun Li is a full professor in School of Mathematical Sciences at Peking University. His main interest is the stochastic modeling and simulation in different fields of science and engineering. His contributions include the multiscale analysis of complex fluids, optimal reduction theory of Markov chain dynamics, and the rare events and landscape theory for chemical reaction kinetics, etc. Currently, he is mainly interested in the scRNA-seq data analysis from dynamical perspectives. Dr. Tiejun Li was the recipient of the NSFC funding for the Excellent and Distinguished Young Scholars. His research results was published in NC, NM, PNAS, PRX, CMP, JCP, SIAM series, ICLR, NeurIPS etc.