Regularized Wasserstein Proximal Algorithms for Nonsmooth Sampling Problems

Learn about regularized Wasserstein proximal algorithms designed to tackle nonsmooth sampling problems in this 42-minute conference talk from IPAM's Scientific Machine Learning Workshop. Explore a novel splitting-based sampling algorithm that addresses the time-implicit discretization of probability flow ODEs, where the score function—defined as the gradient of the logarithm of the current probability density—is approximated using regularized Wasserstein proximal methods. Discover the theoretical foundations including convergence guarantees toward target distributions measured in terms of Renyi divergences under appropriate conditions. Examine numerical experiments demonstrating the algorithm's effectiveness on high-dimensional nonsmooth sampling problems, providing practical insights into this advanced computational approach for scientific machine learning applications.