mlsanityData to 14 Oct 2026

Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems

arXiv 2211.12343 ↗First posted 20 Nov 2022cs.LG cs.CV cs.ITcited by 60

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

Abstract (arXiv)

With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative models. However, while remarkable reconstruction performances have been achieved, their inference time is typically too slow since most of them rely on the seminal diffusion posterior sampling (DPS) framework and thus to approximate the intractable likelihood score, time-consuming gradient calculation through back-propagation is needed. To address this issue, this paper provides a fast and effective solution by proposing a simple closed-form approximation to the likelihood score. For both diffusion and flow-based models, extensive experiments are conducted on various noisy linear inverse problems such as noisy super-resolution, denoising, deblurring, and colorization. In all these tasks, our method (namely DMPS) demonstrates highly competitive or even better reconstruction performances while being significantly faster than all the baseline methods.

Key facts. Cited by 60 papers in the map (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 49 of its 85 references that are in the map. First posted on arXiv 20 Nov 2022.

Builds on

49 of 85 references.

Closest ancestors · 3

Same direction, newest first

  1. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  2. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  3. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 46

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  3. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,177
  4. 2020Denoising Diffusion Implicit Modelscited by 9,781
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  6. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  7. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  8. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  9. 2022Flow Matching for Generative Modelingcited by 5,702
  10. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  11. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  12. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
34 more
  1. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,988
  2. 2015Variational Inference with Normalizing Flowscited by 2,170
  3. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,979
  4. 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,908
  5. 2021Image Super-Resolution via Iterative Refinementcited by 1,511
  6. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,355
  7. 2021Palette: Image-to-Image Diffusion Modelscited by 1,300
  8. 2014Image Super-Resolution Using Deep Convolutional Networkscited by 1,224
  9. 2016Colorful Image Colorizationcited by 1,114
  10. 2017Deep Image Priorcited by 1,098
  11. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
  12. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 635
  13. 2017The Perception-Distortion Tradeoffcited by 587
  14. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 582
  15. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 521
  16. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 433
  17. 2017MoDL: Model Based Deep Learning Architecture for Inverse Problemscited by 387
  18. 2017Compressed Sensing using Generative Modelscited by 339
  19. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Modelscited by 334
  20. 2021Score-based diffusion models for accelerated MRIcited by 311
  21. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 286
  22. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 246
  23. 2020Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulationcited by 225
  24. 2019On instabilities of deep learning in image reconstruction - Does AI come at a cost?cited by 212
  25. 2021Conditional Image Generation with Score-Based Diffusion Modelscited by 197
  26. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  27. 2019Invertible generative models for inverse problems: mitigating representation error and dataset biascited by 94
  28. 2020Solving Linear Inverse Problems Using the Prior Implicit in a Denoisercited by 79
  29. 2019Deep Compressed Sensingcited by 46
  30. 2021Instance-Optimal Compressed Sensing via Posterior Samplingcited by 43
  31. 2017DR2-Net: Deep Residual Reconstruction Network for Image Compressive Sensingcited by 30
  32. 2022Quantized Compressed Sensing with Score-based Generative Modelscited by 15
  33. 2019Global Guarantees for Blind Demodulation with Generative Priorscited by 11
  34. 2013Corrupted Sensing: Novel Guarantees for Separating Structured Signalscited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 14; 2024: 24; 2025: 10; 2026: 12.

60 papers.

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  1. 2023Exploiting Diffusion Prior for Real-World Image Super-Resolutioncited by 489
  2. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistencycited by 182
  3. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 163
  4. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Modelscited by 157
  5. 2023Score-based Data Assimilationcited by 96
  6. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusioncited by 78
  7. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  8. 2024DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Modelscited by 61
  9. 2024On conditional diffusion models for PDE simulationscited by 60
  10. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 46
  11. 2024Generative Diffusion Models for High Dimensional Channel Estimationcited by 26
  12. 2024Learning Spatial Adaptation and Temporal Coherence in Diffusion Models for Video Super-Resolutioncited by 23
38 more
  1. 2023A framework for conditional diffusion modelling with applications in motif scaffolding for protein designcited by 22
  2. 2023Unsupervised Hyperspectral Pansharpening via Low-rank Diffusion Modelcited by 20
  3. 2023Dehazing Ultrasound using Diffusion Modelscited by 17
  4. 2023Removing Structured Noise with Diffusion Modelscited by 14
  5. 2024DiffRetouch: Using Diffusion to Retouch on the Shoulder of Expertscited by 14
  6. 2023Unsupervised speech enhancement with diffusion-based generative modelscited by 12
  7. 2024Posterior Sampling with Denoising Oracles via Tilted Transportcited by 12
  8. 2024On the Asymptotic Mean Square Error Optimality of Diffusion Modelscited by 10
  9. 2024Consistency Model is an Effective Posterior Sample Approximation for Diffusion Inverse Solverscited by 8
  10. 2024State-observation augmented diffusion model for nonlinear assimilation with unknown dynamicscited by 8
  11. 2024Solving Inverse Problems via Diffusion Optimal Controlcited by 8
  12. 2024Unleashing the Denoising Capability of Diffusion Prior for Solving Inverse Problemscited by 7
  13. 2023Inverse problem regularization with hierarchical variational autoencoderscited by 6
  14. 2024Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Samplingcited by 6
  15. 2024Listening to the Noise: Blind Denoising with Gibbs Diffusioncited by 5
  16. 2024Solving General Noisy Inverse Problem via Posterior Sampling: A Policy Gradient Viewpointcited by 5
  17. 2025Conformalized Generative Bayesian Imaging: An Uncertainty Quantification Framework for Computational Imagingcited by 5
  18. 2023QCM-SGM+: Improved Quantized Compressed Sensing With Score-Based Generative Modelscited by 4
  19. 2025Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Learnable Linear Extrapolationcited by 4
  20. 2026Weak Diffusion Priors Can Still Achieve Strong Inverse-Problem Performancecited by 4
  21. 2024Burst Super-Resolution with Diffusion Models for Improving Perceptual Qualitycited by 3
  22. 2025Diff-Unfolding: A Model-Based Score Learning Framework for Inverse Problemscited by 3
  23. 2023Estimating Uncertainty in PET Image Reconstruction via Deep Posterior Samplingcited by 2
  24. 2024Bayesian Conditioned Diffusion Models for Inverse Problemscited by 2
  25. 2024Online Posterior Sampling with a Diffusion Priorcited by 2
  26. 2024Score-Based Variational Inference for Inverse Problemscited by 2
  27. 2025Efficient Burst Super-Resolution with One-step Diffusioncited by 2
  28. 2024Bi-level Guided Diffusion Models for Zero-Shot Medical Imaging Inverse Problemscited by 1
  29. 2024An Unconditional Representation of the Conditional Score in Infinite-Dimensional Linear Inverse Problemscited by 1
  30. 2024Linearly Constrained Diffusion Implicit Modelscited by 1
  31. 2025MAP-based Problem-Agnostic diffusion model for Inverse Problemscited by 1
  32. 2025SAIP: A Plug-and-Play Scale-adaptive Module in Diffusion-based Inverse Problemscited by 1
  33. 2025Robust MIMO Channel Estimation Using Energy-Based Generative Diffusion Modelscited by 1
  34. 2025Generative Spectrum Cartography: Unified Reconstruction and Active Sensing via Diffusion Modelscited by 1
  35. 2026Channel Estimation in MIMO Systems Using Flow Matching Modelscited by 1
  36. 2024Improving Decoupled Posterior Sampling for Inverse Problems using Data Consistency Constraintcited by 0
  37. 2025Posterior Transition Modeling for Unsupervised Diffusion-Based Speech Enhancementcited by 0
  38. 2025Score-Based Turbo Message Passing for Plug-and-Play Compressive Imagingcited by 0

50 most cited of 60 All 60 (JSON)

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  1. 2024Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements
  2. 2025Noise is All You Need: Solving Linear Inverse Problems by Noise Combination Sampling with Diffusion Models
  3. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  4. 2025Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models
  5. 2024Fast Samplers for Inverse Problems in Iterative Refinement Models
  6. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction
  7. 2026Provable diffusion-based posterior sampling for linear inverse problems via DDIM
  8. 2025FlowDPS: Flow-Driven Posterior Sampling for Inverse Problems