# Gradient-free Riemannian Langevin Sampler

arXiv: https://arxiv.org/abs/2607.07519 · HTML: https://mlsanity.com/paper/2607.07519/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 66 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Builds on (most cited first, 16 of 16)

- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [Mirrored Langevin Dynamics](https://mlsanity.com/paper/1802.10174/) (2018)
- [Wasserstein Control of Mirror Langevin Monte Carlo](https://mlsanity.com/paper/2002.04363/) (2020)
- [Langevin diffusions and the Metropolis-adjusted Langevin algorithm](https://mlsanity.com/paper/1309.2983/) (2013)
- [Certified dimension reduction in nonlinear Bayesian inverse problems](https://mlsanity.com/paper/1807.03712/) (2018)
- [Ensemble preconditioning for Markov chain Monte Carlo simulation](https://mlsanity.com/paper/1607.03954/) (2016)
- [Optimal Preconditioning and Fisher Adaptive Langevin Sampling](https://mlsanity.com/paper/2305.14442/) (2023)
- [Derivative-informed neural operator acceleration of geometric MCMC for infinite-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2403.08220/) (2024)
- [Scalable conditional deep inverse Rosenblatt transports using tensor-trains and gradient-based dimension reduction](https://mlsanity.com/paper/2106.04170/) (2021)
- [Adaptive State-Dependent Diffusion for Derivative-Free Optimization](https://mlsanity.com/paper/2302.04370/) (2023)
- [Log-density gradient covariance and automatic metric tensors for Riemann manifold Monte Carlo methods](https://mlsanity.com/paper/2211.01746/) (2022)
- [Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities](https://mlsanity.com/paper/2406.13036/) (2024)
- [A Non-asymptotic Analysis for Learning and Applying a Preconditioner in MCMC](https://mlsanity.com/paper/2602.10714/) (2026)
- [Sampling with Adaptive Variance for Multimodal Distributions](https://mlsanity.com/paper/2411.15220/) (2024)
- [Gradient-enhanced global sensitivity analysis with Poincar'e chaos expansions](https://mlsanity.com/paper/2510.03056/) (2025)
- [Fast-Mixing Markov Chains without Gradients](https://mlsanity.com/paper/2606.27564/) (2026)

## Abstract (arXiv)

We address the problem of efficiently sampling multimodal probability distributions, where standard Markov Chain Monte Carlo methods often suffer from poor mixing and mode trapping. To mitigate these issues, we propose Gradient-free Riemannian Langevin Sampler (GRiLS), a novel proposal that improves exploration without requiring gradient evaluations of the target density. Our approach introduces a Riemannian metric which reshapes the local geometry in order to facilitate transitions across modes. The resulting gradient-free MCMC algorithm is particularly suitable for complex, computationally expensive targets where derivatives are unavailable or impractical. The GRiLS proposal requires knowing the mean and covariance of the target density, which we estimate using an ensemble of interacting particles. Empirical results on multimodal benchmarks demonstrate that GRiLS achieves improved mixing compared to existing gradient-based and gradient-free MCMC approaches.