# Solving Inverse Problems with a Flow-based Noise Model

arXiv: https://arxiv.org/abs/2003.08089 · HTML: https://mlsanity.com/paper/2003.08089/

## Key facts

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

## Built on by (most cited first, 30 of 31)

- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [Prompt-tuning latent diffusion models for inverse problems](https://mlsanity.com/paper/2310.01110/) (2023)
- [GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration](https://mlsanity.com/paper/2301.12686/) (2023)
- [PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization](https://mlsanity.com/paper/2205.12021/) (2022)
- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [Provable Compressed Sensing with Generative Priors via Langevin Dynamics](https://mlsanity.com/paper/2102.12643/) (2021)
- [Removing Structured Noise with Diffusion Models](https://mlsanity.com/paper/2302.05290/) (2023)
- [Robust Stochastically-Descending Unrolled Networks](https://mlsanity.com/paper/2312.15788/) (2023)
- [Optimization for Amortized Inverse Problems](https://mlsanity.com/paper/2210.13983/) (2022)
- [BlindHarmony: "Blind" Harmonization for MR Images via Flow model](https://mlsanity.com/paper/2305.10732/) (2023)
- [Posterior sampling via Langevin dynamics based on generative priors](https://mlsanity.com/paper/2410.02078/) (2024)
- [FunkNN: Neural Interpolation for Functional Generation](https://mlsanity.com/paper/2212.14042/) (2022)
- [NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging Inverse Problems](https://mlsanity.com/paper/2304.08342/) (2023)
- [ICDM: Interference Cancellation Diffusion Models for Wireless Semantic Communications](https://mlsanity.com/paper/2505.19983/) (2025)
- [Differentiable Gaussianization Layers for Inverse Problems Regularized by Deep Generative Models](https://mlsanity.com/paper/2112.03860/) (2021)
- [Equivariant Priors for Compressed Sensing with Unknown Orientation](https://mlsanity.com/paper/2206.14069/) (2022)
- [Deep Injective Prior for Inverse Scattering](https://mlsanity.com/paper/2301.03092/) (2023)
- [Accelerating Inverse Learning via Intelligent Localization with Exploratory Sampling](https://mlsanity.com/paper/2212.01016/) (2022)
- [A Data-Driven Prism: Multi-View Source Separation with Diffusion Model Priors](https://mlsanity.com/paper/2510.05205/) (2025)
- [Generative Flows as a General Purpose Solution for Inverse Problems](https://mlsanity.com/paper/2110.13285/) (2021)
- [Regularized Training of Intermediate Layers for Generative Models for Inverse Problems](https://mlsanity.com/paper/2203.04382/) (2022)
- [Probabilistic Inverse Modeling: An Application in Hydrology](https://mlsanity.com/paper/2210.06213/) (2022)
- [On the Quantification of Image Reconstruction Uncertainty without Training Data](https://mlsanity.com/paper/2311.09639/) (2023)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [Bi-level Guided Diffusion Models for Zero-Shot Medical Imaging Inverse Problems](https://mlsanity.com/paper/2404.03706/) (2024)
- [Tunable Latent Generative Priors for Compressed Sensing and Inverse Problems](https://mlsanity.com/paper/2603.07357/) (2026)
- [SP3: Spherical Priors for Plug-and-Play Restoration](https://mlsanity.com/paper/2606.16396/) (2026)
- [Uncertainty Quantification in Inverse Models in Hydrology](https://mlsanity.com/paper/2310.02193/) (2023)
- [Bayesian imaging inverse problem with SA-Roundtrip prior via HMC-pCN sampler](https://mlsanity.com/paper/2310.17817/) (2023)

## 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.