# Regularization via deep generative models: an analysis point of view

arXiv: https://arxiv.org/abs/2101.08661 · HTML: https://mlsanity.com/paper/2101.08661/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 21 Jan 2021.

## Builds on (most cited first, 14 of 14)

- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Generative Image Inpainting with Contextual Attention](https://mlsanity.com/paper/1801.07892/) (2018)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models](https://mlsanity.com/paper/1703.09912/) (2017)
- [Deep Unfolding of a Proximal Interior Point Method for Image Restoration](https://mlsanity.com/paper/1812.04276/) (2018)
- [Solving Inverse Problems by Joint Posterior Maximization with a VAE Prior](https://mlsanity.com/paper/1911.06379/) (2019)
- [Fast reconstruction of atomic-scale STEM-EELS images from sparse sampling](https://mlsanity.com/paper/2002.01225/) (2020)

## Built on by (most cited first, 5 of 5)

- [Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior](https://mlsanity.com/paper/2103.01648/) (2021)
- [Regularising Inverse Problems with Generative Machine Learning Models](https://mlsanity.com/paper/2107.11191/) (2021)
- [Inverse problem regularization with hierarchical variational autoencoders](https://mlsanity.com/paper/2303.11217/) (2023)
- [Variational Bayes image restoration with compressive autoencoders](https://mlsanity.com/paper/2311.17744/) (2023)
- [Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental study](https://mlsanity.com/paper/2606.14800/) (2026)

## Abstract (arXiv)

This paper proposes a new way of regularizing an inverse problem in imaging (e.g., deblurring or inpainting) by means of a deep generative neural network. Compared to end-to-end models, such approaches seem particularly interesting since the same network can be used for many different problems and experimental conditions, as soon as the generative model is suited to the data. Previous works proposed to use a synthesis framework, where the estimation is performed on the latent vector, the solution being obtained afterwards via the decoder. Instead, we propose an analysis formulation where we directly optimize the image itself and penalize the latent vector. We illustrate the interest of such a formulation by running experiments of inpainting, deblurring and super-resolution. In many cases our technique achieves a clear improvement of the performance and seems to be more robust, in particular with respect to initialization.