# Accelerated Regularized Wasserstein Proximal Sampling Algorithms

arXiv: https://arxiv.org/abs/2601.09848 · HTML: https://mlsanity.com/paper/2601.09848/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 14 Jan 2026.

## Builds on (most cited first, 18 of 18)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights](https://mlsanity.com/paper/1503.01243/) (2015)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [On sampling from a log-concave density using kinetic Langevin diffusions](https://mlsanity.com/paper/1807.09382/) (2018)
- [Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradients](https://mlsanity.com/paper/1905.12247/) (2019)
- [Accelerated Information Gradient flow](https://mlsanity.com/paper/1909.02102/) (2019)
- [Stein Variational Gradient Descent With Matrix-Valued Kernels](https://mlsanity.com/paper/1910.12794/) (2019)
- [Accelerated Flow for Probability Distributions](https://mlsanity.com/paper/1901.03317/) (2019)
- [A kernel formula for regularized Wasserstein proximal operators](https://mlsanity.com/paper/2301.10301/) (2023)
- [Accelerating optimization over the space of probability measures](https://mlsanity.com/paper/2310.04006/) (2023)
- [Hessian-Free High-Resolution Nesterov Acceleration for Sampling](https://mlsanity.com/paper/2006.09230/) (2020)
- [Noise-Free Sampling Algorithms via Regularized Wasserstein Proximals](https://mlsanity.com/paper/2308.14945/) (2023)
- [Laplace Meets Moreau: Smooth Approximation to Infimal Convolutions Using Laplace's Method](https://mlsanity.com/paper/2406.02003/) (2024)
- [Gradient-adjusted underdamped Langevin dynamics for sampling](https://mlsanity.com/paper/2410.08987/) (2024)
- [Tensor train based sampling algorithms for approximating regularized Wasserstein proximal operators](https://mlsanity.com/paper/2401.13125/) (2024)
- [Preconditioned Regularized Wasserstein Proximal Sampling](https://mlsanity.com/paper/2509.01685/) (2025)

## Abstract (arXiv)

We consider sampling from a Gibbs distribution by evolving a finite number of particles using a particular score estimator rather than Brownian motion. To accelerate the particles, we consider a second-order score-based ODE, similar to Nesterov acceleration. In contrast to traditional kernel density score estimation, we use the recently proposed regularized Wasserstein proximal method, yielding the Accelerated Regularized Wasserstein Proximal method (ARWP). We provide a detailed analysis of continuous- and discrete-time non-asymptotic and asymptotic mixing rates for Gaussian initial and target distributions, using techniques from Euclidean acceleration and accelerated information gradients. Compared with the kinetic Langevin sampling algorithm, the proposed algorithm exhibits a higher contraction rate in the asymptotic time regime. Numerical experiments are conducted across various low-dimensional experiments, including multi-modal Gaussian mixtures and ill-conditioned Rosenbrock distributions. ARWP exhibits structured and convergent particles, accelerated discrete-time mixing, and faster tail exploration than the non-accelerated regularized Wasserstein proximal method and kinetic Langevin methods. Additionally, ARWP particles exhibit better generalization properties for some non-log-concave Bayesian neural network tasks.