# Generative Flows as a General Purpose Solution for Inverse Problems

arXiv: https://arxiv.org/abs/2110.13285 · HTML: https://mlsanity.com/paper/2110.13285/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 25 Oct 2021.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [StyleFlow: Attribute-conditioned Exploration of StyleGAN-Generated Images using Conditional Continuous Normalizing Flows](https://mlsanity.com/paper/2008.02401/) (2020)
- [Generative Visual Manipulation on the Natural Image Manifold](https://mlsanity.com/paper/1609.03552/) (2016)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Generative Adversarial Network in Medical Imaging: A Review](https://mlsanity.com/paper/1809.07294/) (2018)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [LOGAN: Latent Optimisation for Generative Adversarial Networks](https://mlsanity.com/paper/1912.00953/) (2019)
- [Solving Inverse Problems with a Flow-based Noise Model](https://mlsanity.com/paper/2003.08089/) (2020)

## Built on by (most cited first, 1 of 1)

- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)

## Abstract (arXiv)

Due to the success of generative flows to model data distributions, they have been explored in inverse problems. Given a pre-trained generative flow, previous work proposed to minimize the 2-norm of the latent variables as a regularization term. The intuition behind it was to ensure high likelihood latent variables that produce the closest restoration. However, high-likelihood latent variables may generate unrealistic samples as we show in our experiments. We therefore propose a solver to directly produce high-likelihood reconstructions. We hypothesize that our approach could make generative flows a general purpose solver for inverse problems. Furthermore, we propose 1 x 1 coupling functions to introduce permutations in a generative flow. It has the advantage that its inverse does not require to be calculated in the generation process. Finally, we evaluate our method for denoising, deblurring, inpainting, and colorization. We observe a compelling improvement of our method over prior works.