In this talk, I will discuss the convergence properties and numerical implementation of the backward regularized Wasserstein proximal (BRWP) method for sampling target distributions. The BRWP method is based on a semi-implicit time discretization of a probability flow ODE, with the score function evolving under the Fokker-Planck equation governing overdamped Langevin dynamics. We employ a kernel-based formulation to approximate the regularized Wasserstein proximal operator and use the Laplace method to establish convergence for log-concave target distributions. Our analysis also identifies optimal step size conditions for achieving convergence. For practical implementation, tensor train approximation is utilized to efficiently handle high-dimensional integration. Numerical experiments further demonstrate the method's convergence and computational efficiency.
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