# Exact Global MCMC with Denoising Diffusion

arXiv: https://arxiv.org/abs/2609.00279 · HTML: https://mlsanity.com/paper/2609.00279/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 25 of 25)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [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)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [Improved sampling via learned diffusions](https://mlsanity.com/paper/2307.01198/) (2023)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [Particle Denoising Diffusion Sampler](https://mlsanity.com/paper/2402.06320/) (2024)
- [Sequential Controlled Langevin Diffusions](https://mlsanity.com/paper/2412.07081/) (2024)
- [Reverse Diffusion Monte Carlo](https://mlsanity.com/paper/2307.02037/) (2023)
- [Stochastic Localization via Iterative Posterior Sampling](https://mlsanity.com/paper/2402.10758/) (2024)
- [Local-Global MCMC kernels: the best of both worlds](https://mlsanity.com/paper/2111.02702/) (2021)
- [Diffusive Gibbs Sampling](https://mlsanity.com/paper/2402.03008/) (2024)
- [Adjoint Schr"odinger Bridge Sampler](https://mlsanity.com/paper/2506.22565/) (2025)
- [Proximal Diffusion Neural Sampler](https://mlsanity.com/paper/2510.03824/) (2025)
- [Improving the evaluation of samplers on multi-modal targets](https://mlsanity.com/paper/2504.08916/) (2025)
- [Markov Chain Monte Carlo with Diffusion Paths](https://mlsanity.com/paper/2607.11631/) (2026)

## Built on by (most cited first, 2 of 2)

- [Local Geometric Mixing via Dobrushin Contraction with Applications to Diffusion Path Monte Carlo and the Proximal Sampler](https://mlsanity.com/paper/2609.28338/) (2026)
- [DAWIS: Data Assimilation with Windowed Inverse Sampling via Multitask Interpolants](https://mlsanity.com/paper/2610.03314/) (2026)

## Abstract (arXiv)

This work shows that diffusion models learned with standard denoising loss can provide effective global MCMC proposals for complex high-dimensional target densities. The method is motivated by the observation that sequentially applying a forward and reverse diffusion process defines a Markov chain with a target stationary distribution for an ideal denoiser trained on samples of the target distribution. This observation can be made exact for any denoiser by applying a Metropolis-Hastings step whose acceptance ratio includes the density of the forward and reverse paths of a discrete time SDE approximation. We therefore propose to train denoising diffusion models on locally convergent MALA samples to learn global MCMC proposals. We call the composition of the global denoiser-based path sampler and a local MALA sampler Denoising Diffusion Monte Carlo (DDMC). Experiments show that DDMC can provide global proposals with high acceptance across a variety of complex target densities. Our results offer preliminary evidence that the established scaling behavior of standard diffusion training transfers directly to exact sampling from high-dimensional unnormalized densities.