# Nonreversible Langevin Samplers: Splitting Schemes, Analysis and Implementation

arXiv: https://arxiv.org/abs/1701.04247 · HTML: https://mlsanity.com/paper/1701.04247/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2017.

## Built on by (most cited first, 8 of 8)

- [Projected Wasserstein gradient descent for high-dimensional Bayesian inference](https://mlsanity.com/paper/2102.06350/) (2021)
- [A Unifying and Canonical Description of Measure-Preserving Diffusions](https://mlsanity.com/paper/2105.02845/) (2021)
- [Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics](https://mlsanity.com/paper/2108.08247/) (2021)
- [Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysis](https://mlsanity.com/paper/2503.19066/) (2025)
- [Fisher information dissipation for time inhomogeneous stochastic differential equations](https://mlsanity.com/paper/2402.01036/) (2024)
- [An operator splitting analysis of Wasserstein--Fisher--Rao gradient flows](https://mlsanity.com/paper/2511.18060/) (2025)
- [Ananke: Contractive Torus Attractor Networks](https://mlsanity.com/paper/2609.24737/) (2026)
- [Generative Modeling with Flux Matching](https://mlsanity.com/paper/2605.07319/) (2026)

## Abstract (arXiv)

For a given target density, there exist an infinite number of diffusion processes which are ergodic with respect to this density. As observed in a number of papers, samplers based on nonreversible diffusion processes can significantly outperform their reversible counterparts both in terms of asymptotic variance and rate of convergence to equilibrium. In this paper, we take advantage of this in order to construct efficient sampling algorithms based on the Lie-Trotter decomposition of a nonreversible diffusion process into reversible and nonreversible components. We show that samplers based on this scheme can significantly outperform standard MCMC methods, at the cost of introducing some controlled bias. In particular, we prove that numerical integrators constructed according to this decomposition are geometrically ergodic and characterise fully their asymptotic bias and variance, showing that the sampler inherits the good mixing properties of the underlying nonreversible diffusion. This is illustrated further with a number of numerical examples ranging from highly correlated low dimensional distributions, to logistic regression problems in high dimensions as well as inference for spatial models with many latent variables.