# Diffusion at Absolute Zero: Langevin Sampling Using Successive Moreau Envelopes [conference paper]

arXiv: https://arxiv.org/abs/2502.01358 · HTML: https://mlsanity.com/paper/2502.01358/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 55 references that are in the map.
- First posted on arXiv 3 Feb 2025.

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [Analysis of Langevin Monte Carlo via convex optimization](https://mlsanity.com/paper/1802.09188/) (2018)
- [On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Models](https://mlsanity.com/paper/1903.12370/) (2019)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Sharp convergence rates for Langevin dynamics in the nonconvex setting](https://mlsanity.com/paper/1805.01648/) (2018)
- [Total Deep Variation for Linear Inverse Problems](https://mlsanity.com/paper/2001.05005/) (2020)
- [Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models](https://mlsanity.com/paper/2202.01479/) (2022)
- [Proximal Markov chain Monte Carlo algorithms](https://mlsanity.com/paper/1306.0187/) (2013)
- [Proximal Langevin Algorithm: Rapid Convergence Under Isoperimetry](https://mlsanity.com/paper/1911.01469/) (2019)
- [Stable Deep MRI Reconstruction using Generative Priors](https://mlsanity.com/paper/2210.13834/) (2022)
- [A Hamilton-Jacobi-based Proximal Operator](https://mlsanity.com/paper/2211.12997/) (2022)
- [Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Non-Convex Optimization](https://mlsanity.com/paper/1904.03537/) (2019)
- [Posterior-Variance-Based Error Quantification for Inverse Problems in Imaging](https://mlsanity.com/paper/2212.12499/) (2022)
- [Subgradient Langevin Methods for Sampling from Non-smooth Potentials](https://mlsanity.com/paper/2308.01417/) (2023)
- [Maximum-a-posteriori estimation with Bayesian confidence regions](https://mlsanity.com/paper/1602.08590/) (2016)
- [Belief Propagation Reloaded: Learning BP-Layers for Labeling Problems](https://mlsanity.com/paper/2003.06258/) (2020)
- [Computed Tomography Reconstruction using Generative Energy-Based Priors](https://mlsanity.com/paper/2203.12658/) (2022)
- [Bregman Proximal Langevin Monte Carlo via Bregman--Moreau Envelopes](https://mlsanity.com/paper/2207.04387/) (2022)
- [Global Solutions to Nonconvex Problems by Evolution of Hamilton-Jacobi PDEs](https://mlsanity.com/paper/2202.11014/) (2022)
- [Total variation on a tree](https://mlsanity.com/paper/1502.07770/) (2015)
- [Ergodicity of Langevin Dynamics and its Discretizations for Non-smooth Potentials](https://mlsanity.com/paper/2411.12051/) (2024)

## Built on by (most cited first, 6 of 6)

- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (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)
- [Time-Inhomogeneous Preconditioned Langevin Dynamics](https://mlsanity.com/paper/2605.06091/) (2026)
- [R'enyi Tracking Bounds for Langevin Dynamics with Moving Targets](https://mlsanity.com/paper/2609.17577/) (2026)

## Abstract (arXiv)

In this article we propose a novel method for sampling from Gibbs distributions of the form π(x)proptoexp(-U(x)) with a potential U(x). In particular, inspired by diffusion models we propose to consider a sequence (πtk)k of approximations of the target density, for which πtk≈ π for k small and, on the other hand, πtk exhibits favorable properties for sampling for k large. This sequence is obtained by replacing parts of the potential U by its Moreau envelopes. Sampling is performed in an Annealed Langevin type procedure, that is, sequentially sampling from πtk for decreasing k, effectively guiding the samples from a simple starting density to the more complex target. In addition to a theoretical analysis we show experimental results supporting the efficacy of the method in terms of increased convergence speed and applicability to multi-modal densities π.