Diffusion Posterior Sampling

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Diffusion posterior sampling uses a learned generative prior and observed data to draw plausible solutions to inverse problems, where measurements may be incomplete or noisy. It is applied to tasks such as image deblurring, inpainting, CT and MRI reconstruction, and scientific problems involving physical systems. Common approaches guide reverse diffusion with likelihood gradients or data-consistency projections, while particle methods, Langevin or Gibbs sampling, and latent-space methods offer alternatives. A central challenge is making samples both faithful to the true posterior and computationally practical: approximate guidance can cause bias, poor uncertainty calibration, or hallucinations, while stronger correction can increase cost or reduce diversity.

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81 papers14 papers in the last four weeks, up 75% on the four weeks before. 0.1% of all new papers.

Optimizing Diffusion Priors in Image Reconstruction from a Single Observation
Apr 22, 2026Frederic Wang, Katherine L. BoumanBayesian Inverse Problems Image Reconstruction
Caltech, Pasadena CA 91125, USA
Noise-Adaptive Diffusion Sampling for Inverse Problems Without Task-Specific Tuning
Apr 18, 2026Yingzhi Xia, Setthakorn Tanomkiattikun, Liangli Zhen +1Markov Chain Monte Carlo Bayesian Inverse Problems
Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore · Agency for Science, Technology and Research, Singapore · Johns Hopkins University +1
Generative Semantic Communication via Alternating Dual-Domain Posterior Sampling
Apr 18, 2026Shunpu Tang, Qianqian YangDiffusion Model Guidance Semantic Communication
College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China
Modelling Gas-Phase Reaction Kinetics with Guided Particle Diffusion Sampling
Apr 8, 2026Andrew Millard, Zheng Zhao, Henrik PedersenPDE Solving Diffusion Posterior Sampling
Division of Statistics and Machine Learning (STIMA), Linköping University, Sweden · STIMA, Linköping University, Sweden · Division of Chemistry, Linköping University, Sweden
Towards Intrinsically Calibrated Uncertainty Quantification in Industrial Data-Driven Models via Diffusion Sampler
Apr 2, 2026Yiran Ma, Jerome Le Ny, Zhichao Chen +1Uncertainty Quantification Uncertainty Calibration
College of Control Science and Engineering, Zhejiang University, Hangzhou, 310027, China · Electrical Engineering Department, Polytechnique Montreal, and with GERAD, Montreal, QC H3T 1J4, Canada · State Key Lab of General AI, School of Intelligence Science and Technology, Peking University, Beijing 100871, China +1
On the role of memorization in learned priors for geophysical inverse problems
Mar 20, 2026Ali Siahkoohi, Davide SabedduMemorization in Generative Models Inverse Problems
University of Central Florida
Robust Physics-Guided Diffusion for Full-Waveform Inversion
Mar 17, 2026Jishen Peng, Enze Jiang, Zheng Ma +1Diffusion-Based Inverse Problems Inverse Problems
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China · Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China · Qing Yuan Research Institute, Shanghai Jiao Tong University, Shanghai, China +2
CT-Conditioned Diffusion Prior with Physics-Constrained Sampling for PET Super-Resolution
Mar 14, 2026Liutao Yang, Zi Wang, Peiyuan Jing +5Medical Image Super-Resolution PET/CT Imaging
Department of Bioengineering and Imperial-X, Imperial College London, London, U.K. · College of Artificial Intelligence, Nanjing University of Aeronautics and Astronautics, Nanjing, China. · School of Engineering, Zurich University of Applied Sciences, Winterthur, Switzerland. +3
Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems
Mar 13, 2026Dibyajyoti Chakraborty, Hojin Kim, Romit MaulikPDE Surrogate Modeling Chaotic Time-Series Prediction
College of Information Sciences and Technology, Pennsylvania State University, University Park, 16802, PA, USA · School of Mechanical Engineering, Purdue University, West Lafayette, 47907, IN, USA
Sparse Scheduled Diffusion Guidance for Inverse Problems
Mar 9, 2026Abduragim Shtanchaev, Albina Ilina, Yazid Janati +3Diffusion-Based Inverse Problems Diffusion Posterior Sampling
MBZUAI, Abu Dhabi, United Arab Emirates · Institute of Foundation Models · EPITA, Paris, France
One step further with Monte-Carlo sampler to guide diffusion better
Mar 4, 2026Minsi Ren, Wenhao Deng, Ruiqi Feng +1Diffusion Model Guidance Diffusion Guidance
AI for Scientific Simulation and Discovery Lab, Westlake University
Calibrated Test-Time Guidance for Bayesian Inference
Feb 25, 2026Daniel Geyfman, Felix Draxler, Jan Groeneveld +3Bayesian Inverse Problems Bayesian Inference
Department of Computer Science, University of California, Irvine, CA, USA · Seoul National University, Seoul, South Korea · Chan-Zuckerberg Initiative, Redwood City, CA, USA
A Gibbs posterior sampler for inverse problem based on prior diffusion model
Feb 11, 2026Jean-François GiovannelliMarkov Chain Monte Carlo Bayesian Inverse Problems
Groupe Signal-Image, IMS (Univ. Bordeaux, CNRS, BINP), Talence, France
Score-based diffusion models for severely ill-posed problems in diffuse optical tomography
Feb 3, 2026Fabian Schneider, Meghdoot Mozumder, Konstantin Tamarov +4Medical Imaging Bayesian Inverse Problems
Department of Computational Engineering, School of Engineering Science LUT University, Finland. · Institute of Analysis and Scientific Computing, TU Wien, Austria. · Department of Technical Physics, Faculty of Science, Forestry and Technology, University of Eastern Finland, Finland. +1
Fundamental Recovery Bounds for SPAD Signals under Stationary Flux
Jan 12, 2026Lior Dvir, Nadav Torem, Mohit Gupta +1Bayesian Inverse Problems Diffusion Posterior Sampling
Viterbi Faculty of Electrical and Computer Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel · Department of Computer Sciences, University of Wisconsin-Madison, Madison, WI 53706, USA
Jacobian-Aware Posterior Sampling for Inverse Problems
Nov 23, 2025Liav Hen, Tom Tirer, Raja Giryes +1Bayesian Inverse Problems Diffusion Guidance
Tel Aviv University, Israel · Bar-Ilan University, Israel · University of Cambridge, UK
DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing
Nov 21, 2025Hao Chen, Renzheng Zhang, Scott S. HowardDiffusion Models for Image Restoration Bayesian Inverse Problems
University of Notre Dame, Notre Dame, IN 46556, USA
A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
Sep 23, 2025Tim Y. J. Wang, O. Deniz AkyildizWasserstein Gradient Flows Bayesian Inverse Problems
Department of Mathematics Imperial College London
Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence
Jul 1, 2025Anantha Narayanan Suresh Babu, Akhil Sadam, Pierre F. J. LermusiauxDiffusion Model Guidance Data Assimilation
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, USA · Center for Computational Science and Engineering, Massachusetts Institute of Technology, Cambridge, USA
Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
Jun 4, 2025Haoxuan Chen, Yinuo Ren, Martin Renqiang Min +2Diffusion Posterior Sampling Bayesian Inverse Problems
ICME, Stanford University, Stanford, CA 94305 · Machine Learning Department, NEC Labs America, Princeton, NJ 08540 · Department of Mathematics and ICME, Stanford University, Stanford, CA 94305
EquiReg: Equivariance Regularized Diffusion for Inverse Problems
May 29, 2025Bahareh Tolooshams, Aditi Chandrashekar, Rayhan Zirvi +4Diffusion Models for Image Restoration Diffusion-Based Inverse Problems
University of Alberta · Alberta Machine, Intelligence Institute (Amii) · Neuroscience and Mental Health Institute, University of Alberta +3

Apr 22, 2026J/K move · Enter open · S save

Optimizing Diffusion Priors in Image Reconstruction from a Single Observation

Frederic Wang, Katherine L. Bouman

Caltech, Pasadena CA 91125, USA

Bayesian Inverse Problems Image Reconstruction Diffusion Model Fine-Tuning Diffusion-Based Inverse Problems Diffusion Posterior Sampling

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While diffusion priors generate high-quality posterior samples across many inverse problems, they are often trained on limited training sets or purely simulated data, thus inheriting the errors and biases of these underlying sources. Current approaches to finetuning diffusion models rely on a large number of observations with varying forward operators, which can be difficult to collect for many applications, and thus lead to overfitting when the measurement set is small. We propose a method for tuning a prior from only a single observation by combining existing diffusion priors into a single product-of-experts prior and identifying the exponents that maximize the Bayesian evidence. We validate our method on real-world inverse problems, including black hole imaging, where the true prior is unknown a priori, and image deblurring with text-conditioned priors. We find that the evidence is often maximized by priors that extend beyond those trained on a single dataset. By generalizing the prior through exponent weighting, our approach enables posterior sampling from both tempered and combined diffusion models, yielding more flexible priors that improve the trustworthiness of the resulting posterior image distribution.