mlsanityData to 7 Oct 2026

SNIPS: Solving Noisy Inverse Problems Stochastically

arXiv 2105.14951 ↗First posted 31 May 2021eess.IV cs.CVcited by 191

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Cited by 131 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise. Our solution incorporates ideas from Langevin dynamics and Newton's method, and exploits a pre-trained minimum mean squared error (MMSE) Gaussian denoiser. The proposed approach relies on an intricate derivation of the posterior score function that includes a singular value decomposition (SVD) of the degradation operator, in order to obtain a tractable iterative algorithm for the desired sampling. Due to its stochasticity, the algorithm can produce multiple high perceptual quality samples for the same noisy observation. We demonstrate the abilities of the proposed paradigm for image deblurring, super-resolution, and compressive sensing. We show that the samples produced are sharp, detailed and consistent with the given measurements, and their diversity exposes the inherent uncertainty in the inverse problem being solved.

Key facts. Cited by 191 papers in the map (data through 7 Oct 2026). Builds on 38 of its 62 references that are in the map. First posted on arXiv 31 May 2021.

Builds on

38 of 62 references.

References · 38

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  5. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  6. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  7. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  8. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  9. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,350
  10. 2018ESRGAN: Enhanced Super-Resolution Generative Adversarial Networkscited by 1,250
  11. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  12. 2017The Perception-Distortion Tradeoffcited by 582
26 more
  1. 2017FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoisingcited by 509
  2. 2021SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Modelscited by 415
  3. 2017Learning Deep CNN Denoiser Prior for Image Restorationcited by 407
  4. 2016Accelerating the Super-Resolution Convolutional Neural Networkcited by 393
  5. 2019DeblurGAN-v2: Deblurring (Orders-of-Magnitude) Faster and Bettercited by 361
  6. 2020PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Modelscited by 358
  7. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  8. 2018Deep Back-Projection Networks For Super-Resolutioncited by 224
  9. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 197
  10. 2020Spatially-Attentive Patch-Hierarchical Network for Adaptive Motion Deblurringcited by 119
  11. 2017Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problemscited by 107
  12. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  13. 2017Deep learning for undersampled MRI reconstructioncited by 91
  14. 2017A Review of Convolutional Neural Networks for Inverse Problems in Imagingcited by 81
  15. 2020Solving Linear Inverse Problems Using the Prior Implicit in a Denoisercited by 78
  16. 2017CNN-Based Projected Gradient Descent for Consistent Image Reconstructioncited by 75
  17. 2018An Online Plug-and-Play Algorithm for Regularized Image Reconstructioncited by 70
  18. 2019Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learningcited by 60
  19. 2017Plug-and-Play Unplugged: Optimization Free Reconstruction using Consensus Equilibriumcited by 58
  20. 2021Stochastic Image Denoising by Sampling from the Posterior Distributioncited by 45
  21. 2019Explorable Super Resolutioncited by 44
  22. 2016Non-Local Color Image Denoising with Convolutional Neural Networkscited by 39
  23. 2017Deep Mean-Shift Priors for Image Restorationcited by 34
  24. 2021High Perceptual Quality Image Denoising with a Posterior Sampling CGANcited by 33
  25. 2015Poisson Inverse Problems by the Plug-and-Play schemecited by 17
  26. 2016Stochastic Quasi-Newton Langevin Monte Carlocited by 14

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 29; 2023: 50; 2024: 51; 2025: 38; 2026: 19.

191 papers.

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  1. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,903
  2. 2023Consistency Modelscited by 1,778
  3. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  4. 2022Diffusion Models in Vision: A Surveycited by 1,008
  5. 2022Denoising Diffusion Restoration Modelscited by 951
  6. 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 526
  7. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  8. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  9. 2022PhysDiff: Physics-Guided Human Motion Diffusion Modelcited by 365
  10. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noisecited by 275
  11. 2021Deblurring via Stochastic Refinementcited by 248
  12. 2024One-Step Effective Diffusion Network for Real-World Image Super-Resolutioncited by 243
38 more
  1. 2022Diffusion models as plug-and-play priorscited by 230
  2. 2022Riemannian Score-Based Generative Modellingcited by 216
  3. 2023Generative Diffusion Prior for Unified Image Restoration and Enhancementcited by 198
  4. 2023Image Restoration with Mean-Reverting Stochastic Differential Equationscited by 182
  5. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  6. 2022Generative Modelling With Inverse Heat Dissipationcited by 164
  7. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 164
  8. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  9. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Modelscited by 156
  10. 2023Manifold Preserving Guided Diffusioncited by 153
  11. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imagingcited by 126
  12. 2022gDDIM: Generalized denoising diffusion implicit modelscited by 125
  13. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 108
  14. 2023Diffusion Models for Image Restoration and Enhancement: A Comprehensive Surveycited by 108
  15. 2022Soft Diffusion: Score Matching for General Corruptionscited by 101
  16. 2023DiffCollage: Parallel Generation of Large Content with Diffusion Modelscited by 100
  17. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
  18. 2023Score-based Data Assimilationcited by 91
  19. 2023Refusion: Enabling Large-Size Realistic Image Restoration with Latent-Space Diffusion Modelscited by 86
  20. 2022Multiscale Structure Guided Diffusion for Image Deblurringcited by 76
  21. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  22. 2023Prompt-tuning latent diffusion models for inverse problemscited by 70
  23. 2023Training-free Linear Image Inverses via Flowscited by 70
  24. 2024Amortizing intractable inference in diffusion models for vision, language, and controlcited by 70
  25. 2024Diffusion Models, Image Super-Resolution And Everything: A Surveycited by 63
  26. 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 60
  27. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 58
  28. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problemscited by 58
  29. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restorationcited by 58
  30. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  31. 2023How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Controlcited by 50
  32. 2022JPEG Artifact Correction using Denoising Diffusion Restoration Modelscited by 45
  33. 2022Deep Equilibrium Approaches to Diffusion Modelscited by 42
  34. 2023Image Restoration Through Generalized Ornstein-Uhlenbeck Bridgecited by 41
  35. 2023Conditional score-based diffusion models for Bayesian inference in infinite dimensionscited by 37
  36. 2024Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learningcited by 35
  37. 2022Enhancing Diffusion-Based Image Synthesis with Robust Classifier Guidancecited by 33
  38. 2023Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Modelscited by 33

50 most cited of 191 All 191 (JSON)