mlsanityData to 7 Oct 2026

Provable Probabilistic Imaging using Score-Based Generative Priors

arXiv 2310.10835 ↗First posted 16 Oct 2023eess.IV cs.CV cs.LGcited by 51

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Cited by 34 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Estimating high-quality images while also quantifying their uncertainty are two desired features in an image reconstruction algorithm for solving ill-posed inverse problems. In this paper, we propose plug-and-play Monte Carlo (PMC) as a principled framework for characterizing the space of possible solutions to a general inverse problem. PMC is able to incorporate expressive score-based generative priors for high-quality image reconstruction while also performing uncertainty quantification via posterior sampling. In particular, we develop two PMC algorithms that can be viewed as the sampling analogues of the traditional plug-and-play priors (PnP) and regularization by denoising (RED) algorithms. To improve the sampling efficiency, we introduce weighted annealing into these PMC algorithms, further developing two additional annealed PMC algorithms (APMC). We establish a theoretical analysis for characterizing the convergence behavior of PMC algorithms. Our analysis provides non-asymptotic stationarity guarantees in terms of the Fisher information, fully compatible with the joint presence of weighted annealing, potentially non-log-concave likelihoods, and imperfect score networks. We demonstrate the performance of the PMC algorithms on multiple representative inverse problems with both linear and nonlinear forward models. Experimental results show that PMC significantly improves reconstruction quality and enables high-fidelity uncertainty quantification.

Key facts. Cited by 51 papers in the map (data through 7 Oct 2026). Builds on 51 of its 79 references that are in the map. First posted on arXiv 16 Oct 2023.

Builds on

51 of 79 references.

References · 51

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  4. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  7. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  8. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  9. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  10. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  11. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  12. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
38 more
  1. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 467
  2. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 464
  3. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  4. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  5. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  6. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  7. 2020End-to-End Variational Networks for Accelerated MRI Reconstructioncited by 201
  8. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 197
  9. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  10. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imagingcited by 126
  11. 2018Regularization by Denoising: Clarifications and New Interpretationscited by 102
  12. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  13. 2022Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imagingcited by 94
  14. 2015Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolationcited by 78
  15. 2019Plug and play methods for magnetic resonance imaging (long version)cited by 75
  16. 2022DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstructioncited by 73
  17. 2018An Online Plug-and-Play Algorithm for Regularized Image Reconstructioncited by 70
  18. 2014From Denoising to Compressed Sensingcited by 67
  19. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problemscited by 65
  20. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  21. 2017Plug-and-Play Unplugged: Optimization Free Reconstruction using Consensus Equilibriumcited by 58
  22. 2020Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imagingcited by 57
  23. 2020Regularization by Denoising via Fixed-Point Projection (RED-PRO)cited by 55
  24. 2020Scalable Plug-and-Play ADMM with Convergence Guaranteescited by 49
  25. 2013Proximal Markov chain Monte Carlo algorithmscited by 46
  26. 2017Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlocited by 43
  27. 2023Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inferencecited by 41
  28. 2020Provable Convergence of Plug-and-Play Priors with MMSE denoiserscited by 39
  29. 2017Deep Mean-Shift Priors for Image Restorationcited by 34
  30. 2019Block Coordinate Regularization by Denoisingcited by 33
  31. 2023Generative Plug and Play: Posterior Sampling for Inverse Problemscited by 24
  32. 2018Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimizationcited by 22
  33. 2021Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Conditioncited by 22
  34. 2021Fixed-Point and Objective Convergence of Plug-and-Play Algorithmscited by 19
  35. 2019SIMBA: Scalable Inversion in Optical Tomography using Deep Denoising Priorscited by 16
  36. 2022On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descentcited by 14
  37. 2020Plug-and-play ISTA converges with kernel denoiserscited by 12
  38. 2020Async-RED: A Provably Convergent Asynchronous Block Parallel Stochastic Method using Deep Denoising Priorscited by 8

50 most cited of 51 All 51 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 16; 2025: 22; 2026: 13.

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  1. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  2. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  3. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
  4. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  5. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 67
  6. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  7. 2024An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observationscited by 20
  8. 2024Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problemscited by 18
  9. 2025Split Gibbs Discrete Diffusion Posterior Samplingcited by 18
  10. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  11. 2024Plug-and-Play image restoration with Stochastic deNOising REgularizationcited by 17
  12. 2024Solving Inverse Problems in Protein Space Using Diffusion-Based Priorscited by 13
38 more
  1. 2024Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problemscited by 7
  2. 2025Inverse Problem Sampling in Latent Space Using Sequential Monte Carlocited by 7
  3. 2025Bifidelity Parameter Estimation Using Conditional Diffusion Modelscited by 7
  4. 2025Unifying and extending Diffusion Models through PDEs for solving Inverse Problemscited by 7
  5. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  6. 2025MRI Super-Resolution with Deep Learning: A Comprehensive Surveycited by 7
  7. 2025Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problemscited by 6
  8. 2024Plug-and-Play Priors as a Score-Based Methodcited by 5
  9. 2025Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problemscited by 5
  10. 2026Generative models for decision-making under distributional shiftcited by 4
  11. 2025STeP: A Framework for Solving Scientific Video Inverse Problems with Spatiotemporal Diffusion Priorscited by 3
  12. 2025A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithmcited by 3
  13. 2025Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priorscited by 3
  14. 2025PSI3D: Plug-and-Play 3D Stochastic Inference with Slice-wise Latent Diffusion Priorcited by 3
  15. 2026Stochastic Generative Plug-and-Play Priorscited by 3
  16. 2024Learning Diffusion Model from Noisy Measurement using Principled Expectation-Maximization Methodcited by 2
  17. 2025Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problemscited by 2
  18. 2025Learning Single Index Models with Diffusion Priorscited by 2
  19. 2025Multitask Learning with Stochastic Interpolantscited by 2
  20. 2026Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamicscited by 2
  21. 2024An Unconditional Representation of the Conditional Score in Infinite-Dimensional Linear Inverse Problemscited by 1
  22. 2024Generalized Compressed Sensing for Image Reconstruction with Diffusion Probabilistic Modelscited by 1
  23. 2025Neural Inverse Scattering with Score-based Regularizationcited by 1
  24. 2025PolyMicros: Bootstrapping a Foundation Model for Polycrystalline Material Structurecited by 1
  25. 2025Injecting Measurement Information Yields a Fast and Noise-Robust Diffusion-Based Inverse Problem Solvercited by 1
  26. 2026DC-LA: Difference-of-Convex Langevin Algorithmcited by 1
  27. 2026Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problemscited by 1
  28. 2026Constrained Particle Seeking: Solving Diffusion Inverse Problems with Just Forward Passescited by 1
  29. 2026Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Frameworkcited by 1
  30. 2026ShuffleFlow: Scalable Posterior Inference for Bayesian Inverse Imagingcited by 1
  31. 2026A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priorscited by 1
  32. 2024Convergence Properties of Score-Based Models for Linear Inverse Problems Using Graduated Optimisationcited by 0
  33. 2024Improving Decoupled Posterior Sampling for Inverse Problems using Data Consistency Constraintcited by 0
  34. 2025QUTCC: Quantile Uncertainty Training and Conformal Calibration for Imaging Inverse Problemscited by 0
  35. 2025Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problemscited by 0
  36. 2026Uncertainty-quantified Pulse Signal Recovery from Facial Video using Regularized Stochastic Interpolantscited by 0
  37. 2026Unbiased Diffusion Variational Inversion via Principled Posterior Matchingcited by 0
  38. 2026Zeroth-Order Non-Log-Concave Sampling with Variance Reduction and Applications to Inverse Problemscited by 0

50 most cited of 51 All 51 (JSON)