# Networks for Nonlinear Diffusion Problems in Imaging

arXiv: https://arxiv.org/abs/1811.12084 · HTML: https://mlsanity.com/paper/1811.12084/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2018.

## Built on by (most cited first, 3 of 3)

- [Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems](https://mlsanity.com/paper/2212.03130/) (2022)
- [Connections between Numerical Algorithms for PDEs and Neural Networks](https://mlsanity.com/paper/2107.14742/) (2021)
- [Invertible ResNets for Inverse Imaging Problems: Competitive Performance with Provable Regularization Properties](https://mlsanity.com/paper/2409.13482/) (2024)

## Abstract (arXiv)

A multitude of imaging and vision tasks have seen recently a major transformation by deep learning methods and in particular by the application of convolutional neural networks. These methods achieve impressive results, even for applications where it is not apparent that convolutions are suited to capture the underlying physics. In this work we develop a network architecture based on nonlinear diffusion processes, named DiffNet. By design, we obtain a nonlinear network architecture that is well suited for diffusion related problems in imaging. Furthermore, the performed updates are explicit, by which we obtain better interpretability and generalisability compared to classical convolutional neural network architectures. The performance of DiffNet tested on the inverse problem of nonlinear diffusion with the Perona-Malik filter on the STL-10 image dataset. We obtain competitive results to the established U-Net architecture, with a fraction of parameters and necessary training data.