mlsanityData to 7 Oct 2026

Composing Normalizing Flows for Inverse Problems

arXiv 2002.11743 ↗First posted 26 Feb 2020stat.ML cs.IT cs.LGcited by 48

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Abstract (arXiv)

Given an inverse problem with a normalizing flow prior, we wish to estimate the distribution of the underlying signal conditioned on the observations. We approach this problem as a task of conditional inference on the pre-trained unconditional flow model. We first establish that this is computationally hard for a large class of flow models. Motivated by this, we propose a framework for approximate inference that estimates the target conditional as a composition of two flow models. This formulation leads to a stable variational inference training procedure that avoids adversarial training. Our method is evaluated on a variety of inverse problems and is shown to produce high-quality samples with uncertainty quantification. We further demonstrate that our approach can be amortized for zero-shot inference.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Feb 2020.

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Citing papers per year: 2021: 4; 2022: 15; 2023: 11; 2024: 7; 2025: 8; 2026: 3.

48 papers.

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  1. 2021Deblurring via Stochastic Refinementcited by 248
  2. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 164
  3. 2023Training-free Linear Image Inverses via Flowscited by 70
  4. 2024Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matchingcited by 50
  5. 2023On Exact Inversion of DPM-Solverscited by 47
  6. 2023WaveDM: Wavelet-Based Diffusion Models for Image Restorationcited by 46
  7. 2021Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpointcited by 32
  8. 2022Generative Visual Prompt: Unifying Distributional Control of Pre-Trained Generative Modelscited by 27
  9. 2022Reliable amortized variational inference with physics-based latent distribution correctioncited by 25
  10. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  11. 2022The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problemscited by 15
  12. 2021Provable Compressed Sensing with Generative Priors via Langevin Dynamicscited by 14
36 more
  1. 2022Conditional Injective Flows for Bayesian Imagingcited by 13
  2. 2022Gradual Domain Adaptation via Normalizing Flowscited by 11
  3. 2024ASPIRE: Iterative Amortized Posterior Inference for Bayesian Inverse Problemscited by 11
  4. 2022VQ-Flows: Vector Quantized Local Normalizing Flowscited by 10
  5. 2023FrePolad: Frequency-Rectified Point Latent Diffusion for Point Cloud Generationcited by 9
  6. 2024Universal Functional Regression with Neural Operator Flowscited by 9
  7. 2023Amortized Normalizing Flows for Transcranial Ultrasound with Uncertainty Quantificationcited by 8
  8. 2023A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensingcited by 7
  9. 2022Optimization for Amortized Inverse Problemscited by 6
  10. 2024Conditional score-based diffusion models for solving inverse problems in mechanicscited by 6
  11. 2022Posterior Matching for Arbitrary Conditioningcited by 4
  12. 2025Conformalized Generative Bayesian Imaging: An Uncertainty Quantification Framework for Computational Imagingcited by 4
  13. 2022AdaAnn: Adaptive Annealing Scheduler for Probability Density Approximationcited by 3
  14. 2022Equivariant Priors for Compressed Sensing with Unknown Orientationcited by 3
  15. 2023Deep Injective Prior for Inverse Scatteringcited by 3
  16. 2025Iterative Flow Matching: Path Correction and Gradual Refinement for Enhanced Generative Modelingcited by 3
  17. 2022Accelerating Inverse Learning via Intelligent Localization with Exploratory Samplingcited by 2
  18. 2022Deep Variational Inverse Scatteringcited by 2
  19. 2023Semi-supervised Learning of Pushforwards For Domain Translation & Adaptationcited by 2
  20. 2024ODE-DPS: ODE-based Diffusion Posterior Sampling for Inverse Problems in Partial Differential Equationcited by 2
  21. 2025Accelerate TarFlow Sampling with GS-Jacobi Iterationcited by 2
  22. 2026Conditional flow matching for physics-constrained inverse problems with finite training datacited by 2
  23. 2021X2CT-FLOW: Maximum a posteriori reconstruction using a progressive flow-based deep generative model for ultra sparse-view computed tomography in ultra low-dose protocolscited by 1
  24. 2022Regularized Training of Intermediate Layers for Generative Models for Inverse Problemscited by 1
  25. 2022Probabilistic Inverse Modeling: An Application in Hydrologycited by 1
  26. 2023On the Quantification of Image Reconstruction Uncertainty without Training Datacited by 1
  27. 2023Learning to sample in Cartesian MRIcited by 1
  28. 2024Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overviewcited by 1
  29. 2024Integrating Generative and Physics-Based Models for Ptychographic Imaging with Uncertainty Quantificationcited by 1
  30. 2025Enhanced Importance Sampling through Latent Space Exploration in Normalizing Flowscited by 1
  31. 2025ReQuestNet: A Foundational Learning model for Channel Estimationcited by 1
  32. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 1
  33. 2022LiP-Flow: Learning Inference-time Priors for Codec Avatars via Normalizing Flows in Latent Spacecited by 0
  34. 2025Bayesian Inverse Problems Meet Flow Matching: Efficient and Flexible Inference via Transformerscited by 0
  35. 2025How Regularization Terms Make Invertible Neural Networks Bayesian Point Estimatorscited by 0
  36. 2026Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantificationcited by 0