# Reverse Diffusion Monte Carlo

arXiv: https://arxiv.org/abs/2307.02037 · HTML: https://mlsanity.com/paper/2307.02037/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 60 references that are in the map.
- First posted on arXiv 5 Jul 2023.

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022)
- [Convergence for score-based generative modeling with polynomial complexity](https://mlsanity.com/paper/2206.06227/) (2022)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [An optimal control perspective on diffusion-based generative modeling](https://mlsanity.com/paper/2211.01364/) (2022)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [Convergence of Langevin MCMC in KL-divergence](https://mlsanity.com/paper/1705.09048/) (2017)
- [Structured Logconcave Sampling with a Restricted Gaussian Oracle](https://mlsanity.com/paper/2010.03106/) (2020)
- [Improved analysis for a proximal algorithm for sampling](https://mlsanity.com/paper/2202.06386/) (2022)
- [Sampling Can Be Faster Than Optimization](https://mlsanity.com/paper/1811.08413/) (2018)
- [Bayesian Learning via Neural Schr"odinger-F"ollmer Flows](https://mlsanity.com/paper/2111.10510/) (2021)
- [On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothness](https://mlsanity.com/paper/2005.13097/) (2020)
- [Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localization](https://mlsanity.com/paper/2203.05093/) (2022)
- [Faster high-accuracy log-concave sampling via algorithmic warm starts](https://mlsanity.com/paper/2302.10249/) (2023)
- [Sampling, Diffusions, and Stochastic Localization](https://mlsanity.com/paper/2305.10690/) (2023)
- [High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm](https://mlsanity.com/paper/1908.10859/) (2019)
- [Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequality](https://mlsanity.com/paper/2303.03589/) (2023)
- [Particle-based Variational Inference with Preconditioned Functional Gradient Flow](https://mlsanity.com/paper/2211.13954/) (2022)
- [When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpoint](https://mlsanity.com/paper/2110.01827/) (2021)
- [Universal Approximation for Log-concave Distributions using Well-conditioned Normalizing Flows](https://mlsanity.com/paper/2107.02951/) (2021)

## Built on by (most cited first, 30 of 41)

- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Review](https://mlsanity.com/paper/2407.13734/) (2024)
- [Particle Denoising Diffusion Sampler](https://mlsanity.com/paper/2402.06320/) (2024)
- [Target Score Matching](https://mlsanity.com/paper/2402.08667/) (2024)
- [Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity](https://mlsanity.com/paper/2405.15986/) (2024)
- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)
- [Stochastic Localization via Iterative Posterior Sampling](https://mlsanity.com/paper/2402.10758/) (2024)
- [Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Sampling](https://mlsanity.com/paper/2407.16936/) (2024)
- [Diffusive Gibbs Sampling](https://mlsanity.com/paper/2402.03008/) (2024)
- [Training Neural Samplers with Reverse Diffusive KL Divergence](https://mlsanity.com/paper/2410.12456/) (2024)
- [Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusion](https://mlsanity.com/paper/2402.17886/) (2024)
- [Outsourced diffusion sampling: Efficient posterior inference in latent spaces of generative models](https://mlsanity.com/paper/2502.06999/) (2025)
- [Proximal Diffusion Neural Sampler](https://mlsanity.com/paper/2510.03824/) (2025)
- [BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matching](https://mlsanity.com/paper/2409.09787/) (2024)
- [Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policies](https://mlsanity.com/paper/2601.08136/) (2026)
- [Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyond](https://mlsanity.com/paper/2502.04575/) (2025)
- [Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamics](https://mlsanity.com/paper/2410.09697/) (2024)
- [Learned Reference-based Diffusion Sampling for multi-modal distributions](https://mlsanity.com/paper/2410.19449/) (2024)
- [Improving the evaluation of samplers on multi-modal targets](https://mlsanity.com/paper/2504.08916/) (2025)
- [Angle Domain Guidance: Latent Diffusion Requires Rotation Rather Than Extrapolation](https://mlsanity.com/paper/2506.11039/) (2025)
- [Control Variate Score Matching for Diffusion Models](https://mlsanity.com/paper/2512.20003/) (2025)
- [Sobolev Regularized MMD Gradient Flow](https://mlsanity.com/paper/2605.11884/) (2026)
- [A Practical Diffusion Path for Sampling](https://mlsanity.com/paper/2406.14040/) (2024)
- [Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusion](https://mlsanity.com/paper/2501.00565/) (2024)
- [Diffusion Path Samplers via Sequential Monte Carlo](https://mlsanity.com/paper/2601.21951/) (2026)
- [Sample-efficient evidence estimation of score based priors for model selection](https://mlsanity.com/paper/2602.20549/) (2026)
- [Discrete diffusion samplers and bridges: Off-policy algorithms and applications in latent spaces](https://mlsanity.com/paper/2602.05961/) (2026)
- [Exact Global MCMC with Denoising Diffusion](https://mlsanity.com/paper/2609.00279/) (2026)
- [New algorithms for sampling and diffusion models](https://mlsanity.com/paper/2406.09665/) (2024)
- [Inflationary Flows: Calibrated Bayesian Inference with Diffusion-Based Models](https://mlsanity.com/paper/2407.08843/) (2024)

## 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.