{"ID":2876045,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.01685","arxiv_id":"2509.01685","title":"Preconditioned Regularized Wasserstein Proximal Sampling","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.","short_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...","url_abs":"https://arxiv.org/abs/2509.01685","url_pdf":"https://arxiv.org/pdf/2509.01685v2","authors":"[\"Hong Ye Tan\",\"Stanley Osher\",\"Wuchen Li\"]","published":"2025-09-01T18:04:31Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.OC\",\"stat.CO\"]","methods":"[\"Diffusion Model\",\"Transformer\"]","has_code":false}