# Wasserstein mixing time of the unadjusted Langevin algorithm

arXiv: https://arxiv.org/abs/2608.02430 · HTML: https://mlsanity.com/paper/2608.02430/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 24 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Analysis of Langevin Monte Carlo via convex optimization](https://mlsanity.com/paper/1802.09188/) (2018)
- [Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem](https://mlsanity.com/paper/1802.08089/) (2018)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Sqrt(d) Dimension Dependence of Langevin Monte Carlo](https://mlsanity.com/paper/2109.03839/) (2021)
- [Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimension](https://mlsanity.com/paper/2108.00682/) (2021)
- [Convergence of Unadjusted Langevin in High Dimensions: Delocalization of Bias](https://mlsanity.com/paper/2408.13115/) (2024)
- [Improved Guarantees for Langevin Monte Carlo with Average Smoothness](https://mlsanity.com/paper/2605.31413/) (2026)

## Built on by (most cited first, 2 of 2)

- [Poisson-Corrector Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling](https://mlsanity.com/paper/2609.12594/) (2026)
- [Near-Linear Accuracy Bounds for Moreau--Yosida Unadjusted Langevin Sampling](https://mlsanity.com/paper/2609.40193/) (2026)

## Abstract (arXiv)

We provide new estimates in Wasserstein distance for the asymptotic bias of the unadjusted Langevin algorithm, in the classical setting of log-smooth strongly log-concave measures. Our bound implies a Wasserstein mixing time of order kappa √d/varepsilon, where kappa is the condition number, d is the dimension, and varepsilon is the target precision: this improves by a factor of √d/varepsilon over the previous state-of-the-art results.