aiqbench analysis
This paper advances Bayesian inference by introducing a rigorous diffusion-based posterior sampling method that eliminates heuristic approximations common in prior work. By leveraging learned score functions and Langevin dynamics within a plug-and-play framework, the approach guarantees convergence for complex, multimodal distributions with provable non-asymptotic error bounds. The methodology represents a significant theoretical step forward for solving inverse problems using generative models without relying on empirical heuristics.
Provable Diffusion Posterior Sampling for Bayesian Inversion
arXiv:2512.08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework. Our approach constructs a probability transport from an easy-to-sample distribution to the target posterior via a diffusion process. To initialize the sampler efficiently, we introduce a warm-start strategy for the particles. The posterior score is then approximated using a Monte Carlo estimator in which samples are generated via Langevin dynamics, avoiding the heuristic approximations prevalent in prior work. The score function driving the Langevin dynamics is learned from data, enabling the model to capture rich structural features of the underlying prior. We also establish non-asymptotic error bounds in Wasserstein-2 distance guaranteeing convergence of the proposed method even for complex, multimodal posterior distributions. We corroborate our theoretical findings with numerical experiments demonstrating the effectiveness of the method across a variety of inverse problems.
Abstract:We propose a novel diffusion-based posterior sampling method within a plug-and-play framework. Our approach constructs a probability transport from an easy-to-sample distribution to the target posterior via a diffusion process. To initialize the sampler efficiently, we introduce a warm-start strategy for the particles. The posterior score is then approximated using a Monte Carlo estimator in which samples are generated via Langevin dynamics, avoiding the heuristic approximations prevalent in prior work. The score function driving the Langevin dynamics is learned from data, enabling the model to capture rich structural features of the underlying prior. We also establish non-asymptotic error bounds in Wasserstein-2 distance guaranteeing convergence of the proposed method even for complex, multimodal posterior distributions. We corroborate our theoretical findings with numerical experiments demonstrating the effectiveness of the method across a variety of inverse problems.
Machine Learning (stat.ML); Machine Learning (cs.LG); Numerical Analysis (math.NA); Probability (math.PR); Statistics Theory (math.ST)
arXiv:2512.08022 [stat.ML]
(or arXiv:2512.08022v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2512.08022 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 237 words
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