# Subgradient Langevin Methods for Sampling from Non-smooth Potentials

arXiv: https://arxiv.org/abs/2308.01417 · HTML: https://mlsanity.com/paper/2308.01417/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2023.

## Built on by (most cited first, 11 of 11)

- [Proximal Interacting Particle Langevin Algorithms](https://mlsanity.com/paper/2406.14292/) (2024)
- [Diffusion at Absolute Zero: Langevin Sampling Using Successive Moreau Envelopes [conference paper]](https://mlsanity.com/paper/2502.01358/) (2025)
- [The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptions](https://mlsanity.com/paper/2502.03458/) (2025)
- [Beyond Scores: Proximal Diffusion Models](https://mlsanity.com/paper/2507.08956/) (2025)
- [Anchored Langevin Algorithms](https://mlsanity.com/paper/2509.19455/) (2025)
- [DC-LA: Difference-of-Convex Langevin Algorithm](https://mlsanity.com/paper/2601.22932/) (2026)
- [Active-Trace Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling](https://mlsanity.com/paper/2608.13467/) (2026)
- [Preconditioned Regularized Wasserstein Proximal Sampling](https://mlsanity.com/paper/2509.01685/) (2025)
- [A proximal gradient algorithm for composite log-concave sampling](https://mlsanity.com/paper/2605.12461/) (2026)
- [Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental study](https://mlsanity.com/paper/2606.14800/) (2026)
- [Muon meets Tamed Langevin: Momentum Preconditioning beyond Convex and gradient-Lipschitz Potentials](https://mlsanity.com/paper/2610.02158/) (2026)

## Abstract (arXiv)

This paper is concerned with sampling from probability distributions π on ℝd admitting a density of the form π(x) propto e-U(x), where U(x)=F(x)+G(Kx) with K being a linear operator and G being non-differentiable. Two different methods are proposed, both employing a subgradient step with respect to Gcirc K, but, depending on the regularity of F, either an explicit or an implicit gradient step with respect to F can be implemented. For both methods, non-asymptotic convergence proofs are provided, with improved convergence results for more regular F. Further, numerical experiments are conducted for simple 2D examples, illustrating the convergence rates, and for examples of Bayesian imaging, showing the practical feasibility of the proposed methods for high dimensional data.