# Noise-Free Sampling Algorithms via Regularized Wasserstein Proximals

arXiv: https://arxiv.org/abs/2308.14945 · HTML: https://mlsanity.com/paper/2308.14945/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 63 references that are in the map.
- First posted on arXiv 28 Aug 2023.

## Builds on (most cited first, 24 of 24)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [Conditional Image Generation with Score-Based Diffusion Models](https://mlsanity.com/paper/2111.13606/) (2021)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem](https://mlsanity.com/paper/1802.08089/) (2018)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [A Tutorial on Kernel Density Estimation and Recent Advances](https://mlsanity.com/paper/1704.03924/) (2017)
- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation](https://mlsanity.com/paper/2006.00702/) (2020)
- [The Modern Mathematics of Deep Learning](https://mlsanity.com/paper/2105.04026/) (2021)
- [Proximal Markov chain Monte Carlo algorithms](https://mlsanity.com/paper/1306.0187/) (2013)
- [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)
- [MCMC Should Mix: Learning Energy-Based Model with Neural Transport Latent Space MCMC](https://mlsanity.com/paper/2006.06897/) (2020)
- [Nonparametric Density Estimation for High-Dimensional Data - Algorithms and Applications](https://mlsanity.com/paper/1904.00176/) (2019)
- [A Hamilton-Jacobi-based Proximal Operator](https://mlsanity.com/paper/2211.12997/) (2022)
- [A kernel formula for regularized Wasserstein proximal operators](https://mlsanity.com/paper/2301.10301/) (2023)
- [Global Optimization via Schr"odinger-F"ollmer Diffusion](https://mlsanity.com/paper/2111.00402/) (2021)

## Built on by (most cited first, 7 of 7)

- [Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference](https://mlsanity.com/paper/2508.12511/) (2025)
- [Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problems](https://mlsanity.com/paper/2409.16471/) (2024)
- [Score-based deterministic density sampling](https://mlsanity.com/paper/2504.18130/) (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)
- [SympFormer: Accelerated attention blocks via Inertial Dynamics on Density Manifolds](https://mlsanity.com/paper/2603.16535/) (2026)
- [Accelerated Regularized Wasserstein Proximal Sampling Algorithms](https://mlsanity.com/paper/2601.09848/) (2026)

## Abstract (arXiv)

We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a stochastic differential equation evolution. The score term is given in closed form by a regularized Wasserstein proximal, using a kernel convolution that is approximated by sampling. We demonstrate fast convergence on various problems and show improved dimensional dependence of mixing time bounds for the case of Gaussian distributions compared to the unadjusted Langevin algorithm (ULA) and the Metropolis-adjusted Langevin algorithm (MALA). We additionally derive closed form expressions for the distributions at each iterate for quadratic potential functions, characterizing the variance reduction. Empirical results demonstrate that the particles behave in an organized manner, lying on level set contours of the potential. Moreover, the posterior mean estimator of the proposed method is shown to be closer to the maximum a-posteriori estimator compared to ULA and MALA in the context of Bayesian logistic regression. Additional examples demonstrate competitive performance for Bayesian neural network training.