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Analyzing Inverse Problems with Invertible Neural Networks

arXiv 1808.04730 ↗First posted 14 Aug 2018cs.LG stat.MLcited by 239

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Abstract (arXiv)

In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse problem is ambiguous: one measurement may map to multiple different sets of parameters. In this setting, the posterior parameter distribution, conditioned on an input measurement, has to be determined. We argue that a particular class of neural networks is well suited for this task -- so-called Invertible Neural Networks (INNs). Although INNs are not new, they have, so far, received little attention in literature. While classical neural networks attempt to solve the ambiguous inverse problem directly, INNs are able to learn it jointly with the well-defined forward process, using additional latent output variables to capture the information otherwise lost. Given a specific measurement and sampled latent variables, the inverse pass of the INN provides a full distribution over parameter space. We verify experimentally, on artificial data and real-world problems from astrophysics and medicine, that INNs are a powerful analysis tool to find multi-modalities in parameter space, to uncover parameter correlations, and to identify unrecoverable parameters.

Key facts. Cited by 239 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Aug 2018.

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Citing papers per year: 2021: 52; 2022: 45; 2023: 57; 2024: 32; 2025: 26; 2026: 27.

239 papers.

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  1. 2021CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flowscited by 320
  2. 2022CDDFuse: Correlation-Driven Dual-Branch Feature Decomposition for Multi-Modality Image Fusioncited by 222
  3. 2023End-to-End Diffusion Latent Optimization Improves Classifier Guidancecited by 107
  4. 2021An Introduction to Deep Generative Modelingcited by 104
  5. 2021Enhanced Invertible Encoding for Learned Image Compressioncited by 102
  6. 2021Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networkscited by 101
  7. 2021Probabilistic Monocular 3D Human Pose Estimation with Normalizing Flowscited by 84
  8. 2021Large-Scale Wasserstein Gradient Flowscited by 76
  9. 2021Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescalingcited by 73
  10. 2021On the Practicality of Deterministic Epistemic Uncertaintycited by 62
  11. 2022Towards Blind Watermarking: Combining Invertible and Non-invertible Mechanismscited by 61
  12. 2023Generalized Teacher Forcing for Learning Chaotic Dynamicscited by 55
38 more
  1. 2021Stochastic Image-to-Video Synthesis using cINNscited by 49
  2. 2021Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networkscited by 48
  3. 2023NIKI: Neural Inverse Kinematics with Invertible Neural Networks for 3D Human Pose and Shape Estimationcited by 45
  4. 2021iPOKE: Poking a Still Image for Controlled Stochastic Video Synthesiscited by 42
  5. 2021Reachability Analysis of Neural Feedback Loopscited by 41
  6. 2023JANA: Jointly Amortized Neural Approximation of Complex Bayesian Modelscited by 41
  7. 2023Generative Sliced MMD Flows with Riesz Kernelscited by 36
  8. 2024Neural Methods for Amortized Inferencecited by 36
  9. 2022Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problemscited by 34
  10. 2021Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpointcited by 32
  11. 2023Transformed Distribution Matching for Missing Value Imputationcited by 31
  12. 2022Universal approximation property of invertible neural networkscited by 30
  13. 2024Recent Advances on Machine Learning for Computational Fluid Dynamics: A Surveycited by 27
  14. 2021Benchmarking Invertible Architectures on Inverse Problemscited by 25
  15. 2022Semi-supervised Invertible Neural Operators for Bayesian Inverse Problemscited by 25
  16. 2023Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernelcited by 25
  17. 2021Conditional Invertible Neural Networks for Diverse Image-to-Image Translationcited by 24
  18. 2021Generalized Normalizing Flows via Markov Chainscited by 23
  19. 2022Residual Skill Policies: Learning an Adaptable Skill-based Action Space for Reinforcement Learning for Roboticscited by 23
  20. 2022PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularizationcited by 22
  21. 2023Consistency Models for Scalable and Fast Simulation-Based Inferencecited by 22
  22. 2021Generative Networks for Precision Enthusiastscited by 21
  23. 2022An unfolding method based on conditional Invertible Neural Networks (cINN) using iterative trainingcited by 20
  24. 2022Fully probabilistic deep models for forward and inverse problems in parametric PDEscited by 19
  25. 2022Learning to Immunize Images for Tamper Localization and Self-Recoverycited by 19
  26. 2022Towards Bidirectional Arbitrary Image Rescaling: Joint Optimization and Cycle Idempotencecited by 18
  27. 2022Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systemscited by 18
  28. 2024On the Universality of Volume-Preserving and Coupling-Based Normalizing Flowscited by 18
  29. 2021Understanding Event-Generation Networks via Uncertaintiescited by 17
  30. 2023Lifting Architectural Constraints of Injective Flowscited by 17
  31. 2021No-Reference Image Quality Assessment by Hallucinating Pristine Featurescited by 16
  32. 2021Parallelised Diffeomorphic Sampling-based Motion Planningcited by 16
  33. 2021Deconvolutional Networks on Graph Datacited by 16
  34. 2022Autoinverse: Uncertainty Aware Inversion of Neural Networkscited by 16
  35. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 16
  36. 2023Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoderscited by 16
  37. 2021Inverse design of two-dimensional materials with invertible neural networkscited by 15
  38. 2021Robust Inverse Framework using Knowledge-guided Self-Supervised Learning: An application to Hydrologycited by 15

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