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Solving Inverse Problems with a Flow-based Noise Model

arXiv 2003.08089 ↗First posted 18 Mar 2020cs.LG cs.IT math.ITcited by 31

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Abstract (arXiv)

We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with arbitrary dependencies as well as non-linear forward operators. We empirically validate the efficacy of our method on various inverse problems, including compressed sensing with quantized measurements and denoising with highly structured noise patterns. We also present initial theoretical recovery guarantees for solving inverse problems with a flow prior.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). First posted on arXiv 18 Mar 2020.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 7; 2023: 11; 2024: 4; 2025: 4; 2026: 2.

31 papers.

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  1. 2024D-Flow: Differentiating through Flows for Controlled Generationcited by 122
  2. 2023Training-free Linear Image Inverses via Flowscited by 72
  3. 2023Prompt-tuning latent diffusion models for inverse problemscited by 70
  4. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restorationcited by 59
  5. 2022PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularizationcited by 22
  6. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  7. 2021Provable Compressed Sensing with Generative Priors via Langevin Dynamicscited by 14
  8. 2023Removing Structured Noise with Diffusion Modelscited by 14
  9. 2023Robust Stochastically-Descending Unrolled Networkscited by 9
  10. 2022Optimization for Amortized Inverse Problemscited by 6
  11. 2023BlindHarmony: "Blind" Harmonization for MR Images via Flow modelcited by 5
  12. 2024Posterior sampling via Langevin dynamics based on generative priorscited by 5
19 more
  1. 2022FunkNN: Neural Interpolation for Functional Generationcited by 4
  2. 2023NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging Inverse Problemscited by 4
  3. 2025ICDM: Interference Cancellation Diffusion Models for Wireless Semantic Communicationscited by 4
  4. 2021Differentiable Gaussianization Layers for Inverse Problems Regularized by Deep Generative Modelscited by 3
  5. 2022Equivariant Priors for Compressed Sensing with Unknown Orientationcited by 3
  6. 2023Deep Injective Prior for Inverse Scatteringcited by 3
  7. 2022Accelerating Inverse Learning via Intelligent Localization with Exploratory Samplingcited by 2
  8. 2025A Data-Driven Prism: Multi-View Source Separation with Diffusion Model Priorscited by 2
  9. 2021Generative Flows as a General Purpose Solution for Inverse Problemscited by 1
  10. 2022Regularized Training of Intermediate Layers for Generative Models for Inverse Problemscited by 1
  11. 2022Probabilistic Inverse Modeling: An Application in Hydrologycited by 1
  12. 2023On the Quantification of Image Reconstruction Uncertainty without Training Datacited by 1
  13. 2024Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overviewcited by 1
  14. 2024Bi-level Guided Diffusion Models for Zero-Shot Medical Imaging Inverse Problemscited by 1
  15. 2026Tunable Latent Generative Priors for Compressed Sensing and Inverse Problemscited by 1
  16. 2026SP3: Spherical Priors for Plug-and-Play Restorationcited by 1
  17. 2023Uncertainty Quantification in Inverse Models in Hydrologycited by 0
  18. 2023Bayesian imaging inverse problem with SA-Roundtrip prior via HMC-pCN samplercited by 0
  19. 2025Beyond Invisibility: Learning Robust Visible Watermarks for Stronger Copyright Protectioncited by 0