# Tensor train based sampling algorithms for approximating regularized Wasserstein proximal operators

arXiv: https://arxiv.org/abs/2401.13125 · HTML: https://mlsanity.com/paper/2401.13125/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2024.

## Built on by (most cited first, 4 of 4)

- [Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme](https://mlsanity.com/paper/2506.01502/) (2025)
- [HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models](https://mlsanity.com/paper/2409.09614/) (2024)
- [Preconditioned Regularized Wasserstein Proximal Sampling](https://mlsanity.com/paper/2509.01685/) (2025)
- [Accelerated Regularized Wasserstein Proximal Sampling Algorithms](https://mlsanity.com/paper/2601.09848/) (2026)

## Abstract (arXiv)

We present a tensor train (TT) based algorithm designed for sampling from a target distribution and employ TT approximation to capture the high-dimensional probability density evolution of overdamped Langevin dynamics. This involves utilizing the regularized Wasserstein proximal operator, which exhibits a simple kernel integration formulation, i.e., the softmax formula of the traditional proximal operator. The integration, performed in ℝd, poses a challenge in practical scenarios, making the algorithm practically implementable only with the aid of TT approximation. In the specific context of Gaussian distributions, we rigorously establish the unbiasedness and linear convergence of our sampling algorithm towards the target distribution. To assess the effectiveness of our proposed methods, we apply them to various scenarios, including Gaussian families, Gaussian mixtures, bimodal distributions, and Bayesian inverse problems in numerical examples. The sampling algorithm exhibits superior accuracy and faster convergence when compared to classical Langevin dynamics-type sampling algorithms.