mlsanityData to 7 Oct 2026

Score-Based Diffusion Models as Principled Priors for Inverse Imaging

arXiv 2304.11751 ↗First posted 23 Apr 2023cs.CVcited by 126

On the map: Diffusion models → Inverse problems and image restoration

Abstract (arXiv)

Priors are essential for reconstructing images from noisy and/or incomplete measurements. The choice of the prior determines both the quality and uncertainty of recovered images. We propose turning score-based diffusion models into principled image priors ("score-based priors") for analyzing a posterior of images given measurements. Previously, probabilistic priors were limited to handcrafted regularizers and simple distributions. In this work, we empirically validate the theoretically-proven probability function of a score-based diffusion model. We show how to sample from resulting posteriors by using this probability function for variational inference. Our results, including experiments on denoising, deblurring, and interferometric imaging, suggest that score-based priors enable principled inference with a sophisticated, data-driven image prior.

Key facts. Cited by 126 papers in the map (data through 7 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 58 of its 89 references that are in the map. First posted on arXiv 23 Apr 2023.

Builds on

58 of 89 references.

Closest ancestors · 5

Same direction, newest first

  1. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration20 Mar
  2. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  3. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  4. 2022Denoising Diffusion Restoration Models27 Jan
  5. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 53

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  8. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  9. 2022Classifier-Free Diffusion Guidancecited by 5,717
  10. 2022Generative Adversarial Networkscited by 5,603
  11. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  12. 2013Auto-Encoding Variational Bayescited by 3,980
38 more
  1. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  4. 2021GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Modelscited by 3,595
  5. 2016Density estimation using Real NVPcited by 2,029
  6. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  7. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  8. 2016Variational Inference: A Review for Statisticianscited by 1,466
  9. 2016Context Encoders: Feature Learning by Inpaintingcited by 1,424
  10. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,155
  11. 2021Variational Diffusion Modelscited by 1,145
  12. 2017Deep Image Priorcited by 1,097
  13. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  14. 2016Pixel Recurrent Neural Networkscited by 814
  15. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  16. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  17. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  18. 2018Free-Form Image Inpainting with Gated Convolutioncited by 594
  19. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  20. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  21. 2018Do Deep Generative Models Know What They Don't Know?cited by 443
  22. 2018Invertible Residual Networkscited by 364
  23. 2021Score-based diffusion models for accelerated MRIcited by 308
  24. 2015MADE: Masked Autoencoder for Distribution Estimationcited by 306
  25. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  26. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  27. 2022On Neural Differential Equationscited by 264
  28. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 258
  29. 2022Diffusion models as plug-and-play priorscited by 230
  30. 2020Why Normalizing Flows Fail to Detect Out-of-Distribution Datacited by 220
  31. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  32. 2015Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inferencecited by 159
  33. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  34. 2022Deep Image Deblurring: A Surveycited by 94
  35. 2019Invertible generative models for inverse problems: mitigating representation error and dataset biascited by 93
  36. 2022Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matchingcited by 79
  37. 2020Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imagingcited by 57
  38. 2022Enhancing Diffusion-Based Image Synthesis with Robust Classifier Guidancecited by 33

50 most cited of 53 All 53 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 17; 2024: 47; 2025: 40; 2026: 22.

126 papers.

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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. 2023Diffusion Models for Image Restoration and Enhancement: A Comprehensive Surveycited by 108
  4. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
  5. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  6. 2023Prompt-tuning latent diffusion models for inverse problemscited by 70
  7. 2024Amortizing intractable inference in diffusion models for vision, language, and controlcited by 70
  8. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 67
  9. 2024Estimating Epistemic and Aleatoric Uncertainty with a Single Modelcited by 52
  10. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  11. 2024Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matchingcited by 50
  12. 2023CG3D: Compositional Generation for Text-to-3D via Gaussian Splattingcited by 42
38 more
  1. 2024Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariancecited by 42
  2. 2023Image Restoration Through Generalized Ornstein-Uhlenbeck Bridgecited by 41
  3. 2024Neural Network Diffusioncited by 39
  4. 2024Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learningcited by 35
  5. 2024Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Datacited by 32
  6. 2025Does FLUX Already Know How to Perform Physically Plausible Image Composition?cited by 30
  7. 2023Generative Plug and Play: Posterior Sampling for Inverse Problemscited by 24
  8. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
  9. 2023Towards Real-World Blind Face Restoration with Generative Diffusion Priorcited by 21
  10. 2024Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problemscited by 21
  11. 2024An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observationscited by 20
  12. 2025Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posteriorcited by 20
  13. 2025UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Controlcited by 18
  14. 2025Split Gibbs Discrete Diffusion Posterior Samplingcited by 18
  15. 2023Dehazing Ultrasound using Diffusion Modelscited by 17
  16. 2023Variational Bayesian Imaging with an Efficient Surrogate Score-based Priorcited by 16
  17. 2023Uncertainty Quantification via Neural Posterior Principal Componentscited by 16
  18. 2024Conditional LoRA Parameter Generationcited by 16
  19. 2023Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstructioncited by 15
  20. 2024Repulsive Latent Score Distillation for Solving Inverse Problemscited by 15
  21. 2025Diffusion models for inverse problemscited by 15
  22. 2024Free Hunch: Denoiser Covariance Estimation for Diffusion Models Without Extra Costscited by 14
  23. 2024Osmosis: RGBD Diffusion Prior for Underwater Image Restorationcited by 13
  24. 2024Invertible Diffusion Models for Compressed Sensingcited by 12
  25. 2024Posterior Sampling with Denoising Oracles via Tilted Transportcited by 12
  26. 2024Integrating Amortized Inference with Diffusion Models for Learning Clean Distribution from Corrupted Imagescited by 12
  27. 2024CoSIGN: Few-Step Guidance of ConSIstency Model to Solve General INverse Problemscited by 12
  28. 2024ASPIRE: Iterative Amortized Posterior Inference for Bayesian Inverse Problemscited by 11
  29. 2024Efficient Prior Calibration From Indirect Datacited by 11
  30. 2025IRBridge: Solving Image Restoration Bridge with Pre-trained Generative Diffusion Modelscited by 11
  31. 2023Adapt and Diffuse: Sample-adaptive Reconstruction via Latent Diffusion Modelscited by 9
  32. 2023Self-Supervised Scalable Deep Compressed Sensingcited by 8
  33. 2024PQMass: Probabilistic Assessment of the Quality of Generative Models using Probability Mass Estimationcited by 8
  34. 2024Consistency Model is an Effective Posterior Sample Approximation for Diffusion Inverse Solverscited by 8
  35. 2024Think Twice Before You Act: Improving Inverse Problem Solving With MCMCcited by 8
  36. 2024Patch-Based Diffusion Models Beat Whole-Image Models for Mismatched Distribution Inverse Problemscited by 8
  37. 2025Multiscale guidance of protein structure prediction with heterogeneous cryo-EM datacited by 8
  38. 2024Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problemscited by 7

50 most cited of 126 All 126 (JSON)

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  1. 2026Optimizing Diffusion Priors in Image Reconstruction from a Single Observation
  2. 2023Score-based Diffusion Models for Bayesian Image Reconstruction
  3. 2026Sample-efficient evidence estimation of score based priors for model selection
  4. 2026A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
  5. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models
  6. 2024Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models
  7. 2025Diff-Unfolding: A Model-Based Score Learning Framework for Inverse Problems
  8. 2023Removing Structured Noise with Diffusion Models