mlsanityData to 7 Oct 2026

Reverse Diffusion Monte Carlo

arXiv 2307.02037 ↗First posted 5 Jul 2023stat.ML cs.LG math.OCcited by 41

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Abstract (arXiv)

We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching problem into a mean estimation one. By estimating the means of the regularized posterior distributions, we derive a novel Monte Carlo sampling algorithm called reverse diffusion Monte Carlo (rdMC), which is distinct from the Markov chain Monte Carlo (MCMC) methods. We determine the sample size from the error tolerance and the properties of the posterior distribution to yield an algorithm that can approximately sample the target distribution with any desired accuracy. Additionally, we demonstrate and prove under suitable conditions that sampling with rdMC can be significantly faster than that with MCMC. For multi-modal target distributions such as those in Gaussian mixture models, rdMC greatly improves over the Langevin-style MCMC sampling methods both theoretically and in practice. The proposed rdMC method offers a new perspective and solution beyond classical MCMC algorithms for the challenging complex distributions.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). Builds on 30 of its 60 references that are in the map. First posted on arXiv 5 Jul 2023.

Builds on

30 of 60 references.

References · 30

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  5. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 440
  6. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 242
  7. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  8. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptionscited by 215
  9. 2022Convergence of score-based generative modeling for general data distributionscited by 179
  10. 2022Convergence for score-based generative modeling with polynomial complexitycited by 176
  11. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
  12. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
18 more
  1. 2023Denoising Diffusion Samplerscited by 144
  2. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 131
  3. 2018Log-concave sampling: Metropolis-Hastings algorithms are fastcited by 117
  4. 2019Theoretical guarantees for sampling and inference in generative models with latent diffusionscited by 97
  5. 2017Convergence of Langevin MCMC in KL-divergencecited by 86
  6. 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 85
  7. 2022Improved analysis for a proximal algorithm for samplingcited by 72
  8. 2018Sampling Can Be Faster Than Optimizationcited by 68
  9. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
  10. 2020On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothnesscited by 55
  11. 2022Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localizationcited by 48
  12. 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 44
  13. 2023Sampling, Diffusions, and Stochastic Localizationcited by 38
  14. 2019High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithmcited by 36
  15. 2023Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequalitycited by 31
  16. 2022Particle-based Variational Inference with Preconditioned Functional Gradient Flowcited by 20
  17. 2021When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpointcited by 12
  18. 2021Universal Approximation for Log-concave Distributions using Well-conditioned Normalizing Flowscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 20; 2025: 10; 2026: 11.

41 papers.

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  1. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  2. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 92
  3. 2024Particle Denoising Diffusion Samplercited by 63
  4. 2024Target Score Matchingcited by 46
  5. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  6. 2024Model-Based Diffusion for Trajectory Optimizationcited by 30
  7. 2024Stochastic Localization via Iterative Posterior Samplingcited by 27
  8. 2024Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Samplingcited by 23
  9. 2024Diffusive Gibbs Samplingcited by 21
  10. 2024Training Neural Samplers with Reverse Diffusive KL Divergencecited by 21
  11. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusioncited by 19
  12. 2025Outsourced diffusion sampling: Efficient posterior inference in latent spaces of generative modelscited by 16
29 more
  1. 2025Proximal Diffusion Neural Samplercited by 16
  2. 2024BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matchingcited by 14
  3. 2025Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyondcited by 11
  4. 2024Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamicscited by 10
  5. 2024Learned Reference-based Diffusion Sampling for multi-modal distributionscited by 9
  6. 2025Improving the evaluation of samplers on multi-modal targetscited by 9
  7. 2025Angle Domain Guidance: Latent Diffusion Requires Rotation Rather Than Extrapolationcited by 8
  8. 2026Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policiescited by 7
  9. 2024A Practical Diffusion Path for Samplingcited by 5
  10. 2024Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusioncited by 4
  11. 2025Control Variate Score Matching for Diffusion Modelscited by 4
  12. 2026Sample-efficient evidence estimation of score based priors for model selectioncited by 3
  13. 2026Sobolev Regularized MMD Gradient Flowcited by 3
  14. 2026Diffusion Path Samplers via Sequential Monte Carlocited by 2
  15. 2026Discrete diffusion samplers and bridges: Off-policy algorithms and applications in latent spacescited by 2
  16. 2024New algorithms for sampling and diffusion modelscited by 1
  17. 2024Inflationary Flows: Calibrated Bayesian Inference with Diffusion-Based Modelscited by 1
  18. 2025Restricted Spectral Gap Decomposition for Simulated Tempering Targeting Mixture Distributionscited by 1
  19. 2025Sampling by averaging: A multiscale approach to score estimationcited by 1
  20. 2026Alternating Diffusion for Proximal Sampling with Zeroth Order Queriescited by 1
  21. 2026Conditional Diffusion Samplingcited by 1
  22. 2026Exact Global MCMC with Denoising Diffusioncited by 1
  23. 2024An Improved Analysis of Langevin Algorithms with Prior Diffusion for Non-Log-Concave Samplingcited by 0
  24. 2024Denoising Fisher Training For Neural Implicit Samplerscited by 0
  25. 2025Improved sampling algorithms and functional inequalities for non-log-concave distributionscited by 0
  26. 2025LSAM: Asynchronous Distributed Training with Landscape-Smoothed Sharpness-Aware Minimizationcited by 0
  27. 2026Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEscited by 0
  28. 2026Sampling from multi-modal distributions on Riemannian manifolds with training-free stochastic interpolantscited by 0
  29. 2026Total Variation Guarantees for Sampling with Stochastic Localizationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2022Denoising MCMC for Accelerating Diffusion-Based Generative Models
  2. 2025Likelihood Matching for Diffusion Models
  3. 2024Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference
  4. 2023MCMC-Correction of Score-Based Diffusion Models for Model Composition
  5. 2024Diffusion Generative Modelling for Divide-and-Conquer MCMC
  6. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models
  7. 2023Accelerating Markov Chain Monte Carlo sampling with diffusion models
  8. 2025Distributional Diffusion Models with Scoring Rules