Markov Chain Monte Carlo with Diffusion Paths

• URL: http://arxiv.org/abs/2607.11631v1
• Date: Mon, 13 Jul 2026 14:48:19 GMT
• Title: Markov Chain Monte Carlo with Diffusion Paths
• Abstract summary: Sampling from multimodal distributions is a longstanding challenge for local Markov chain Monte Carlo methods.<n>We propose interpolating along the diffusion path, the marginals of a noising diffusion process that carries the target toward a Gaussian.<n>We show that MAD-Path improves global exploration and mode-weight estimation relative to tempering-based MCMC methods and unadjusted diffusion samplers.
• Score: 16.16991829228785
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sampling from multimodal distributions is a longstanding challenge for classical local Markov chain Monte Carlo (MCMC) methods. A popular remedy is to introduce a sequence of intermediate distributions that interpolate between the target and a simpler reference. The classical choice, tempering, raises the density to a power, but distorts the relative weights of asymmetric modes and can lead to poor mixing. We instead propose interpolating along the diffusion path, the marginals of a noising diffusion process that carries the target toward a Gaussian. This path preserves the relative weights of the modes and enjoys favorable mixing properties, which we make precise through a spectral-gap analysis of the corresponding ideal transition kernel. Sampling along the path requires its intermediate scores, which can be estimated from the unnormalized target through variational approaches, yielding only an approximate sampler. To remove the resulting bias, we introduce the Metropolis-adjusted diffusion path (MAD-Path) sampler, which corrects the diffusion-path proposal in an augmented path space and leaves the target invariant regardless of the accuracy of the learned score or the discretization error. We further quantify how these two errors affect the acceptance probability, providing guidance for practical tuning. Experiments on a range of Bayesian posteriors show that MAD-Path improves global exploration and mode-weight estimation relative to tempering-based MCMC methods and unadjusted diffusion samplers.

Related papers

• Exact Global MCMC with Denoising Diffusion [3.763882712747131]
  We train diffusion models on locally convergent MALA samples to learn global MCMC proposals.<n>Experiments show that Denoising Diffusion Monte Carlo (DDMC) can provide global proposals with high acceptance across a variety of complex target densities.
  arXiv  Detail & Related papers  (2026-08-31T19:24:36Z)
• A Unified View of Drifting and Score-Based Models [92.51878018325031]
  We make our relationship to the score-matching principle behind diffusion models precise by showing that drifting admits a score-based formulation on kernel-smoothed distributions.<n>We derive an exact decomposition for general radial kernels, and for the Laplace kernel we prove rigorous error bounds showing that drifting remains an accurate proxy for score matching in low-temperature and high-dimensional regimes.
  arXiv  Detail & Related papers  (2026-03-08T07:41:36Z)
• Diffusion Alignment Beyond KL: Variance Minimisation as Effective Policy Optimiser [35.260598916253635]
  We introduce Variance Minimisation Policy optimisation (VMPO)<n>VMPO formulates diffusion alignment as minimising the variance of log importance weights.<n>Under different choices of potential functions and variance minimisation strategies, VMPO recovers various existing methods.
  arXiv  Detail & Related papers  (2026-02-12T18:06:03Z)
• Diffusion Path Samplers via Sequential Monte Carlo [0.31690235522182103]
  We develop a diffusion-based sampler for target distributions known up to a normalising constant.<n>Our approach is based on a practical implementation of diffusion-annealed Langevin Monte Carlo.<n>We provide theoretical guarantees and empirically demonstrate the effectiveness of our method on several synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2026-01-29T16:32:12Z)
• Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts [64.34482582690927]
  We provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models.<n>We propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality.
  arXiv  Detail & Related papers  (2025-03-04T17:46:51Z)
• Amortized Posterior Sampling with Diffusion Prior Distillation [55.03585818289934]
  Amortized Posterior Sampling is a novel variational inference approach for efficient posterior sampling in inverse problems.<n>Our method trains a conditional flow model to minimize the divergence between the variational distribution and the posterior distribution implicitly defined by the diffusion model.<n>Unlike existing methods, our approach is unsupervised, requires no paired training data, and is applicable to both Euclidean and non-Euclidean domains.
  arXiv  Detail & Related papers  (2024-07-25T09:53:12Z)
• Sequential Monte Carlo for Inclusive KL Minimization in Amortized Variational Inference [3.126959812401426]
  We propose SMC-Wake, a procedure for fitting an amortized variational approximation that uses sequential Monte Carlo samplers to estimate the gradient of the inclusive KL divergence. In experiments with both simulated and real datasets, SMC-Wake fits variational distributions that approximate the posterior more accurately than existing methods.
  arXiv  Detail & Related papers  (2024-03-15T18:13:48Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Differentiating Metropolis-Hastings to Optimize Intractable Densities [51.16801956665228]
  We develop an algorithm for automatic differentiation of Metropolis-Hastings samplers. We apply gradient-based optimization to objectives expressed as expectations over intractable target densities.
  arXiv  Detail & Related papers  (2023-06-13T17:56:02Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Sampling from high-dimensional, multimodal distributions using automatically tuned, tempered Hamiltonian Monte Carlo [0.0]
  Hamiltonian Monte Carlo (HMC) is widely used for sampling from high dimensional target distributions with densities known up to proportionality.<n>We propose a method that combines tempering with HMC to enable efficient sampling from high dimensional, strongly multimodal distributions.
  arXiv  Detail & Related papers  (2021-11-12T18:48:36Z)
• Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence [77.06203118175335]
  Variational Inference (VI) is a popular alternative to exact sampling in Bayesian inference. Importance sampling (IS) is often used to fine-tune and de-bias the estimates of approximate Bayesian inference procedures. We propose a novel combination of optimization and sampling techniques for approximate Bayesian inference.
  arXiv  Detail & Related papers  (2021-06-30T11:00:24Z)
• Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC [83.48593305367523]
  Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. We introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.
  arXiv  Detail & Related papers  (2021-02-04T02:21:08Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.