# Provable Diffusion Posterior Sampling for Bayesian Inversion

arXiv: https://arxiv.org/abs/2512.08022 · HTML: https://mlsanity.com/paper/2512.08022/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2025.

## Built on by (most cited first, 10 of 10)

- [Inference-Time Alignment for Diffusion Models via Variationally Stable Doob's Matching](https://mlsanity.com/paper/2601.06514/) (2026)
- [Image Restoration via Diffusion Models with Dynamic Resolution](https://mlsanity.com/paper/2605.14267/) (2026)
- [A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors](https://mlsanity.com/paper/2608.15144/) (2026)
- [Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEs](https://mlsanity.com/paper/2601.08527/) (2026)
- [Beyond Expected Information Gain: Stable Bayesian Optimal Experimental Design with Integral Probability Metrics and Plug-and-Play Extensions](https://mlsanity.com/paper/2604.21849/) (2026)
- [Proximal-Based Generative Modeling for Bayesian Inverse Problems](https://mlsanity.com/paper/2605.13278/) (2026)
- [Tracing the Oracle: Improving Diffusion Timestep Scheduling for 3D CT Reconstruction](https://mlsanity.com/paper/2606.06236/) (2026)
- [Direct Intermediate Initialization for Tilted Diffusion Samplers](https://mlsanity.com/paper/2610.06834/) (2026)
- [Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme](https://mlsanity.com/paper/2610.10278/) (2026)
- [Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing](https://mlsanity.com/paper/2610.11834/) (2026)

## Abstract (arXiv)

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.