mlsanityData to 14 Oct 2026

Improved analysis for a proximal algorithm for sampling

arXiv 2202.06386 ↗First posted 13 Feb 2022math.ST stat.ML stat.THcited by 73

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Abstract (arXiv)

We study the proximal sampler of Lee, Shen, and Tian (2021) and obtain new convergence guarantees under weaker assumptions than strong log-concavity: namely, our results hold for (1) weakly log-concave targets, and (2) targets satisfying isoperimetric assumptions which allow for non-log-concavity. We demonstrate our results by obtaining new state-of-the-art sampling guarantees for several classes of target distributions. We also strengthen the connection between the proximal sampler and the proximal method in optimization by interpreting the proximal sampler as an entropically regularized Wasserstein proximal method, and the proximal point method as the limit of the proximal sampler with vanishing noise.

Key facts. Cited by 73 papers in the map (data through 14 Oct 2026). Builds on 18 of its 48 references that are in the map. First posted on arXiv 13 Feb 2022.

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18 of 48 references.

References · 18

  1. 2014Convex Optimization: Algorithms and Complexitycited by 575
  2. 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 539
  3. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 227
  4. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 127
  5. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  6. 2018Log-concave sampling: Metropolis-Hastings algorithms are fastcited by 118
  7. 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 86
  8. 2020Wasserstein Control of Mirror Langevin Monte Carlocited by 55
  9. 2020Efficient constrained sampling via the mirror-Langevin algorithmcited by 55
  10. 2019Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradientscited by 51
  11. 2013Proximal Markov chain Monte Carlo algorithmscited by 46
  12. 2020Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithmcited by 35
6 more
  1. 2019Proximal Langevin Algorithm: Rapid Convergence Under Isoperimetrycited by 34
  2. 2021A Proximal Algorithm for Sampling from Non-smooth Potentialscited by 24
  3. 2019Efficient MCMC Sampling with Dimension-Free Convergence Rate using ADMM-type Splittingcited by 22
  4. 2016Auxiliary gradient-based sampling algorithmscited by 21
  5. 2021The query complexity of sampling from strongly log-concave distributions in one dimensioncited by 18
  6. 2020Langevin Monte Carlo: random coordinate descent and variance reductioncited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 5; 2023: 13; 2024: 19; 2025: 21; 2026: 15.

73 papers.

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  1. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 445
  2. 2023The probability flow ODE is provably fastcited by 146
  3. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 97
  4. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 68
  5. 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 45
  6. 2023Reverse Diffusion Monte Carlocited by 41
  7. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  8. 2023Improved dimension dependence of a proximal algorithm for samplingcited 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. 2022A Proximal Algorithm for Samplingcited by 22
  12. 2024Diffusive Gibbs Samplingcited by 21
38 more
  1. 2022Regularized Stein Variational Gradient Flowcited by 19
  2. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusioncited by 19
  3. 2024In-and-Out: Algorithmic Diffusion for Sampling Convex Bodiescited by 19
  4. 2024U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Modelscited by 17
  5. 2026High-accuracy sampling for diffusion models and log-concave distributionscited by 16
  6. 2023Improved Sample Complexity Bounds for Diffusion Model Trainingcited by 14
  7. 2022Fisher information lower bounds for samplingcited by 12
  8. 2023Private (Stochastic) Non-Convex Optimization Revisited: Second-Order Stationary Points and Excess Riskscited by 12
  9. 2023Query lower bounds for log-concave samplingcited by 12
  10. 2024Sampling and Integration of Logconcave Functions by Algorithmic Diffusioncited by 12
  11. 2025Mixing Time of the Proximal Sampler in Relative Fisher Information via Strong Data Processing Inequalitycited by 12
  12. 2024Fast Convergence of Phi-Divergence Along the Unadjusted Langevin Algorithm and Proximal Samplercited by 11
  13. 2023Algorithmic Aspects of the Log-Laplace Transform and a Non-Euclidean Proximal Samplercited by 10
  14. 2024GIST: Gibbs self-tuning for locally adaptive Hamiltonian Monte Carlocited by 9
  15. 2024Proximal Interacting Particle Langevin Algorithmscited by 8
  16. 2025A Sharp KL-Convergence Analysis for Diffusion Models under Minimal Assumptionscited by 8
  17. 2024Sampling from the Mean-Field Stationary Distributioncited by 7
  18. 2025Faster logconcave sampling from a cold start in high dimensioncited by 7
  19. 2024Proximal Oracles for Optimization and Samplingcited by 6
  20. 2024A Separation in Heavy-Tailed Sampling: Gaussian vs. Stable Oracles for Proximal Samplerscited by 6
  21. 2024Characterizing Dependence of Samples along the Langevin Dynamics and Algorithms via Contraction of Phi-Mutual Informationcited by 5
  22. 2024Faster Sampling via Stochastic Gradient Proximal Samplercited by 5
  23. 2025Algorithm- and Data-Dependent Generalization Bounds for Diffusion Modelscited by 5
  24. 2026On Forgetting and Stability of Score-based Generative modelscited by 5
  25. 2023Mean-Square Analysis of Discretized Ito Diffusions for Heavy-tailed Samplingcited by 4
  26. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  27. 2024Convergence of Unadjusted Langevin in High Dimensions: Delocalization of Biascited by 4
  28. 2024R'enyi-infinity constrained sampling with d3 membership queriescited by 3
  29. 2025Beyond Scores: Proximal Diffusion Modelscited by 3
  30. 2025A Non-Asymptotic Convergent Analysis for Scored-Based Graph Generative Model via a System of Stochastic Differential Equationscited by 3
  31. 2025Oracle-based Uniform Sampling from Convex Bodiescited by 3
  32. 2026A unified complexity bound for logconcave samplingcited by 3
  33. 2022A Proximal Algorithm for Sampling from Non-convex Potentialscited by 2
  34. 2024Covariance estimation using Markov chain Monte Carlocited by 2
  35. 2025Convergence Analysis of the Wasserstein Proximal Algorithm beyond Geodesic Convexitycited by 2
  36. 2025Perspectives on Stochastic Localizationcited by 2
  37. 2025A Gradient Guided Diffusion Framework for Chance Constrained Programmingcited by 2
  38. 2025Gradient Flow Sampler-based Distributionally Robust Optimizationcited by 2

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