Preconditioned Regularized Wasserstein Proximal Sampling

Hong Ye Tan; Stanley Osher; Wuchen Li

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arXiv · 2509.01685

Preconditioned Regularized Wasserstein Proximal Sampling

Hong Ye Tan·Stanley Osher·Wuchen Li

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Abstract

We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed by approximating the score function with the numerically tractable score of a regularized Wasserstein proximal operator. This is derived by a Cole--Hopf transformation on coupled anisotropic heat equations, yielding a kernel formulation for the preconditioned regularized Wasserstein proximal. The diffusion component of the proposed method is also interpreted as a modified self-attention block, as in transformer architectures. For quadratic potentials, we provide a discrete-time non-asymptotic convergence analysis and explicitly characterize the bias, which is dependent on regularization and independent of step-size. Experiments demonstrate acceleration and particle-level stability on various log-concave and non-log-concave toy examples to Bayesian total-variation regularized image deconvolution, and competitive/better performance on non-convex Bayesian neural network training when utilizing variable preconditioning matrices.

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BibTeX RIS

Hong Ye Tan, Stanley Osher, Wuchen Li. 2025-09-01. Preconditioned Regularized Wasserstein Proximal Sampling. https://arxiv.org/abs/2509.01685

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