# Generative networks as inverse problems with Scattering transforms

arXiv: https://arxiv.org/abs/1805.06621 · HTML: https://mlsanity.com/paper/1805.06621/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2018.

## Built on by (most cited first, 6 of 6)

- [Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transforms](https://mlsanity.com/paper/2104.11244/) (2021)
- [Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces](https://mlsanity.com/paper/2205.14627/) (2022)
- [Modelling nonlinear dependencies in the latent space of inverse scattering](https://mlsanity.com/paper/2203.10307/) (2022)
- [Deep Invertible Approximation of Topologically Rich Maps between Manifolds](https://mlsanity.com/paper/2210.00577/) (2022)
- [Hyperspectral Reconstruction of Skin Through Fusion of Scattering Transform Features](https://mlsanity.com/paper/2404.10030/) (2024)
- [SCRAPL: Scattering Transform with Random Paths for Machine Learning](https://mlsanity.com/paper/2602.11145/) (2026)

## Abstract (arXiv)

Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but the underlying mathematics are not well understood. We compute deep convolutional network generators by inverting a fixed embedding operator. Therefore, they do not require to be optimized with a discriminator or an encoder. The embedding is Lipschitz continuous to deformations so that generators transform linear interpolations between input white noise vectors into deformations between output images. This embedding is computed with a wavelet Scattering transform. Numerical experiments demonstrate that the resulting Scattering generators have similar properties as GANs or VAEs, without learning a discriminative network or an encoder.