# When and How Can Deep Generative Models be Inverted?

arXiv: https://arxiv.org/abs/2006.15555 · HTML: https://mlsanity.com/paper/2006.15555/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2020.

## Built on by (most cited first, 8 of 8)

- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [Stochastic Image Denoising by Sampling from the Posterior Distribution](https://mlsanity.com/paper/2101.09552/) (2021)
- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Universal Joint Approximation of Manifolds and Densities by Simple Injective Flows](https://mlsanity.com/paper/2110.04227/) (2021)
- [Adversarial robustness of sparse local Lipschitz predictors](https://mlsanity.com/paper/2202.13216/) (2022)
- [Closed-Loop Transcription via Convolutional Sparse Coding](https://mlsanity.com/paper/2302.09347/) (2023)
- [Signal Recovery with Non-Expansive Generative Network Priors](https://mlsanity.com/paper/2204.13599/) (2022)
- [A Survey on Leveraging Pre-trained Generative Adversarial Networks for Image Editing and Restoration](https://mlsanity.com/paper/2207.10309/) (2022)

## Abstract (arXiv)

Deep generative models (e.g. GANs and VAEs) have been developed quite extensively in recent years. Lately, there has been an increased interest in the inversion of such a model, i.e. given a (possibly corrupted) signal, we wish to recover the latent vector that generated it. Building upon sparse representation theory, we define conditions that are applicable to any inversion algorithm (gradient descent, deep encoder, etc.), under which such generative models are invertible with a unique solution. Importantly, the proposed analysis is applicable to any trained model, and does not depend on Gaussian i.i.d. weights. Furthermore, we introduce two layer-wise inversion pursuit algorithms for trained generative networks of arbitrary depth, and accompany these with recovery guarantees. Finally, we validate our theoretical results numerically and show that our method outperforms gradient descent when inverting such generators, both for clean and corrupted signals.