In this talk, we introduce regularized Wasserstein proximal algorithms for nonsmooth sampling problems. We propose a splitting-based sampling algorithm for the time-implicit discretization of the probability flow ODE. In this approach, the score function, defined as the gradient of the logarithm of the current probability density, is approximated using the regularized Wasserstein proximal. We establish convergence towards the target distribution in terms of Renyi divergences under suitable conditions. Finally, we demonstrate the effectiveness of our method through numerical experiments on high-dimensional nonsmooth sampling problems.
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