mlsanityData to 14 Oct 2026

Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm

arXiv 1507.05021 ↗First posted 17 Jul 2015math.ST stat.CO stat.MEcited by 197

Not on the map. Why?

Cited by 25 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

In this paper, we study a method to sample from a target distribution π over ℝd having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler discretization of the overdamped Langevin stochastic differential equation associated with π. For both constant and decreasing step sizes in the Euler discretization, we obtain non-asymptotic bounds for the convergence to the target distribution π in total variation distance. A particular attention is paid to the dependency on the dimension d, to demonstrate the applicability of this method in the high dimensional setting. These bounds improve and extend the results of (Dalalyan 2014).

Key facts. Cited by 197 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 Jul 2015.

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Citing papers per year: 2021: 26; 2022: 32; 2023: 30; 2024: 35; 2025: 41; 2026: 33.

197 papers.

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  1. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 602
  2. 2022Convergence of denoising diffusion models under the manifold hypothesiscited by 242
  3. 2022Convergence for score-based generative modeling with polynomial complexitycited by 177
  4. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 97
  5. 2021Differential Privacy Dynamics of Langevin Diffusion and Noisy Gradient Descentcited by 73
  6. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  7. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 60
  8. 2022Convex Analysis of the Mean Field Langevin Dynamicscited by 55
  9. 2021Separation of Scales and a Thermodynamic Description of Feature Learning in Some CNNscited by 53
  10. 2024Langevin Unlearning: A New Perspective of Noisy Gradient Descent for Machine Unlearningcited by 49
  11. 2025Inference-time Scaling of Diffusion Models through Classical Searchcited by 49
  12. 2023Grokking as a First Order Phase Transition in Two Layer Networkscited by 48
38 more
  1. 2021Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Samplingcited by 44
  2. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecastingcited by 43
  3. 2021KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Supportcited by 37
  4. 2021The Mirror Langevin Algorithm Converges with Vanishing Biascited by 37
  5. 2022FedPop: A Bayesian Approach for Personalised Federated Learningcited by 35
  6. 2023Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequalitycited by 31
  7. 2025Accelerated Diffusion Models via Speculative Samplingcited by 31
  8. 2022Birth-death dynamics for sampling: Global convergence, approximations and their asymptoticscited by 30
  9. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distancecited by 29
  10. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 28
  11. 2024Stochastic Localization via Iterative Posterior Samplingcited by 28
  12. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  13. 2021Sqrt(d) Dimension Dependence of Langevin Monte Carlocited by 25
  14. 2022Convergence of the Riemannian Langevin Algorithmcited by 25
  15. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 22
  16. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  17. 2021The query complexity of sampling from strongly log-concave distributions in one dimensioncited by 18
  18. 2023Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimationcited by 17
  19. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  20. 2025LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimizationcited by 16
  21. 2023When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?cited by 15
  22. 2023Chain of Log-Concave Markov Chainscited by 14
  23. 2024Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalitiescited by 13
  24. 2024Entropy contraction of the Gibbs sampler under log-concavitycited by 13
  25. 2021Asymmetric Heavy Tails and Implicit Bias in Gaussian Noise Injectionscited by 12
  26. 2021When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpointcited by 12
  27. 2022Fisher information lower bounds for samplingcited by 12
  28. 2023Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Casecited by 12
  29. 2023Query lower bounds for log-concave samplingcited by 12
  30. 2025Mixing Time of the Proximal Sampler in Relative Fisher Information via Strong Data Processing Inequalitycited by 12
  31. 2021Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networkscited by 11
  32. 2021DG-LMC: A Turn-key and Scalable Synchronous Distributed MCMC Algorithm via Langevin Monte Carlo within Gibbscited by 11
  33. 2021Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimensioncited by 11
  34. 2022The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distributioncited by 11
  35. 2023Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithmcited by 11
  36. 2023Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisitedcited by 10
  37. 2023Geometric Neural Diffusion Processescited by 10
  38. 2024Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlocited by 10

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