mlsanityData to 7 Oct 2026

Removing Structured Noise with Diffusion Models

arXiv 2302.05290 ↗First posted 20 Jan 2023cs.LG eess.IV eess.SPcited by 14

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

Abstract (arXiv)

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

Key facts. Cited by 14 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 37 of its 60 references that are in the map. First posted on arXiv 20 Jan 2023.

Builds on

37 of 60 references.

Closest ancestors · 6

Same direction, newest first

  1. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  2. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems20 Nov
  3. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  4. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  5. 2022Denoising Diffusion Restoration Models27 Jan
  6. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 31

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2022Classifier-Free Diffusion Guidancecited by 5,717
  7. 2022Generative Adversarial Networkscited by 5,603
  8. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  9. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  10. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  11. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  12. 2016Density estimation using Real NVPcited by 2,029
19 more
  1. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  2. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  3. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  4. 2021Score-based Generative Modeling in Latent Spacecited by 634
  5. 2017The Perception-Distortion Tradeoffcited by 582
  6. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  7. 2017Compressed Sensing using Generative Modelscited by 337
  8. 2022Understanding Diffusion Models: A Unified Perspectivecited by 337
  9. 2021Score-based diffusion models for accelerated MRIcited by 308
  10. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  11. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noisecited by 275
  12. 2019Progressive Image Deraining Networks: A Better and Simpler Baselinecited by 271
  13. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  14. 2022Soft Diffusion: Score Matching for General Corruptionscited by 101
  15. 2019Invertible generative models for inverse problems: mitigating representation error and dataset biascited by 93
  16. 2022Subspace Diffusion Generative Modelscited by 70
  17. 2021Instance-Optimal Compressed Sensing via Posterior Samplingcited by 43
  18. 2020Solving Inverse Problems with a Flow-based Noise Modelcited by 31
  19. 2021Deep Unfolding with Normalizing Flow Priors for Inverse Problemscited by 23

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 6; 2025: 3; 2026: 1.

14 papers.

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By area:

  1. 2024Variational Diffusion Posterior Sampling with Midpoint Guidancecited by 32
  2. 2023Dehazing Ultrasound using Diffusion Modelscited by 17
  3. 2023Score Priors Guided Deep Variational Inference for Unsupervised Real-World Single Image Denoisingcited by 15
  4. 2023SDDPM: Speckle Denoising Diffusion Probabilistic Modelscited by 6
  5. 2024Listening to the Noise: Blind Denoising with Gibbs Diffusioncited by 5
  6. 2024Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Samplingcited by 5
  7. 2025ICDM: Interference Cancellation Diffusion Models for Wireless Semantic Communicationscited by 4
  8. 2024Active inference and deep generative modeling for cognitive ultrasoundcited by 3
  9. 2025High Volume Rate 3D Ultrasound Reconstruction with Diffusion Modelscited by 2
  10. 2025A Data-Driven Prism: Multi-View Source Separation with Diffusion Model Priorscited by 2
  11. 2023AT-2FF: Adaptive Type-2 Fuzzy Filter for De-noising Images Corrupted with Salt-and-Peppercited by 0
  12. 2024Prototype Clustered Diffusion Models for Versatile Inverse Problemscited by 0
2 more
  1. 2024DM-SBL: Channel Estimation under Structured Interferencecited by 0
  2. 2026Iterative Amortized Hierarchical VAEcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithm
  2. 2024A Survey on Diffusion Models for Inverse Problems
  3. 2025Noise is All You Need: Solving Linear Inverse Problems by Noise Combination Sampling with Diffusion Models
  4. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models
  5. 2024Learning Diffusion Model from Noisy Measurement using Principled Expectation-Maximization Method
  6. 2024Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements
  7. 2025Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions
  8. 2023Diffusion with Forward Models: Solving Stochastic Inverse Problems Without Direct Supervision