# Regularising Inverse Problems with Generative Machine Learning Models

arXiv: https://arxiv.org/abs/2107.11191 · HTML: https://mlsanity.com/paper/2107.11191/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 70 of its 130 references that are in the map.
- First posted on arXiv 22 Jul 2021.

## Builds on (most cited first, 30 of 70)

- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models](https://mlsanity.com/paper/2003.03808/) (2020)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [Pros and Cons of GAN Evaluation Measures](https://mlsanity.com/paper/1802.03446/) (2018)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Image Processing Using Multi-Code GAN Prior](https://mlsanity.com/paper/1912.07116/) (2019)
- [Semantic Image Inpainting with Deep Generative Models](https://mlsanity.com/paper/1607.07539/) (2016)
- [i-RevNet: Deep Invertible Networks](https://mlsanity.com/paper/1802.07088/) (2018)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [An Introduction to Deep Generative Modeling](https://mlsanity.com/paper/2103.05180/) (2021)
- [Adversarial Regularizers in Inverse Problems](https://mlsanity.com/paper/1805.11572/) (2018)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [Beyond Face Rotation: Global and Local Perception GAN for Photorealistic and Identity Preserving Frontal View Synthesis](https://mlsanity.com/paper/1704.04086/) (2017)

## Built on by (most cited first, 22 of 22)

- [A Neural-Network-Based Convex Regularizer for Inverse Problems](https://mlsanity.com/paper/2211.12461/) (2022)
- [PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization](https://mlsanity.com/paper/2205.12021/) (2022)
- [Manifold Learning by Mixture Models of VAEs for Inverse Problems](https://mlsanity.com/paper/2303.15244/) (2023)
- [Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstruction](https://mlsanity.com/paper/2308.14409/) (2023)
- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (2025)
- [Compressed Sensing MRI Reconstruction Regularized by VAEs with Structured Image Covariance](https://mlsanity.com/paper/2210.14586/) (2022)
- [Variational Bayes image restoration with compressive autoencoders](https://mlsanity.com/paper/2311.17744/) (2023)
- [Iteratively Refined Image Reconstruction with Learned Attentive Regularizers](https://mlsanity.com/paper/2407.06608/) (2024)
- [Error Analysis of Bayesian Inverse Problems with Generative Priors](https://mlsanity.com/paper/2601.17374/) (2026)
- [Conditional flow matching for physics-constrained inverse problems with finite training data](https://mlsanity.com/paper/2603.14135/) (2026)
- [A Stability Benchmark of Generative Regularizers for Inverse Problems](https://mlsanity.com/paper/2605.10076/) (2026)
- [Deep priors for satellite image restoration with accurate uncertainties](https://mlsanity.com/paper/2412.04130/) (2024)
- [A Diffusion-Based Generative Prior Approach to Sparse-view Computed Tomography](https://mlsanity.com/paper/2602.10722/) (2026)
- [Weakly Convex Ridge Regularization for 3D Non-Cartesian MRI Reconstruction](https://mlsanity.com/paper/2603.27158/) (2026)
- [Adversarial Generative NMF for Single Channel Source Separation](https://mlsanity.com/paper/2305.01758/) (2023)
- [Multibranch Generative Models for Multichannel Imaging with an Application to PET/CT Synergistic Reconstruction](https://mlsanity.com/paper/2404.08748/) (2024)
- [Maximum Discrepancy Generative Regularization and Non-Negative Matrix Factorization for Single Channel Source Separation](https://mlsanity.com/paper/2404.15296/) (2024)
- [RELD: Regularization by Latent Diffusion Models for Image Restoration](https://mlsanity.com/paper/2503.22563/) (2025)
- [Enhancing Obsolescence Forecasting with Deep Generative Data Augmentation: A Semi-Supervised Framework for Low-Data Industrial Applications](https://mlsanity.com/paper/2505.01261/) (2025)
- [Allure of Craquelure: A Variational-Generative Approach to Crack Detection in Paintings](https://mlsanity.com/paper/2602.09730/) (2026)
- [FlowADMM: Plug-and-play ADMM with Flow-based Renoise-Denoise Priors](https://mlsanity.com/paper/2605.08640/) (2026)
- [Diffusion Graph Posterior Sampling for Nonlinear Inverse Problems with Application to Electrical Impedance Tomography](https://mlsanity.com/paper/2605.19621/) (2026)

## Abstract (arXiv)

Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The considered regularisers penalise images that are far from the range of a generative model that has learned to produce images similar to a training dataset. We name this family textitgenerative regularisers. The success of generative regularisers depends on the quality of the generative model and so we propose a set of desired criteria to assess generative models and guide future research. In our numerical experiments, we evaluate three common generative models, autoencoders, variational autoencoders and generative adversarial networks, against our desired criteria. We also test three different generative regularisers on the inverse problems of deblurring, deconvolution, and tomography. We show that restricting solutions of the inverse problem to lie exactly in the range of a generative model can give good results but that allowing small deviations from the range of the generator produces more consistent results.