# Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration

arXiv: https://arxiv.org/abs/1508.02848 · HTML: https://mlsanity.com/paper/1508.02848/

## Key facts

- Cited by 195 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2015.

## Built on by (most cited first, 30 of 195)

- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Diffusion Models for Image Restoration and Enhancement: A Comprehensive Survey](https://mlsanity.com/paper/2308.09388/) (2023)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Practical Blind Image Denoising via Swin-Conv-UNet and Data Synthesis](https://mlsanity.com/paper/2203.13278/) (2022)
- [Towards Flexible Blind JPEG Artifacts Removal](https://mlsanity.com/paper/2109.14573/) (2021)
- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [CiaoSR: Continuous Implicit Attention-in-Attention Network for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2212.04362/) (2022)
- [Invertible Denoising Network: A Light Solution for Real Noise Removal](https://mlsanity.com/paper/2104.10546/) (2021)
- [Masked Image Training for Generalizable Deep Image Denoising](https://mlsanity.com/paper/2303.13132/) (2023)
- [C2N: Practical Generative Noise Modeling for Real-World Denoising](https://mlsanity.com/paper/2202.09533/) (2022)
- [Dynamic Attentive Graph Learning for Image Restoration](https://mlsanity.com/paper/2109.06620/) (2021)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [Stochastic Image Denoising by Sampling from the Posterior Distribution](https://mlsanity.com/paper/2101.09552/) (2021)
- [CVF-SID: Cyclic multi-Variate Function for Self-Supervised Image Denoising by Disentangling Noise from Image](https://mlsanity.com/paper/2203.13009/) (2022)
- [Model-Based Image Signal Processors via Learnable Dictionaries](https://mlsanity.com/paper/2201.03210/) (2022)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [Multi-stage image denoising with the wavelet transform](https://mlsanity.com/paper/2209.12394/) (2022)
- [On Measuring and Controlling the Spectral Bias of the Deep Image Prior](https://mlsanity.com/paper/2107.01125/) (2021)
- [Random Sub-Samples Generation for Self-Supervised Real Image Denoising](https://mlsanity.com/paper/2307.16825/) (2023)
- [Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms](https://mlsanity.com/paper/2308.10542/) (2023)
- [Unsupervised Image Denoising in Real-World Scenarios via Self-Collaboration Parallel Generative Adversarial Branches](https://mlsanity.com/paper/2308.06776/) (2023)
- [Learning a Model-Driven Variational Network for Deformable Image Registration](https://mlsanity.com/paper/2105.12227/) (2021)
- [Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior](https://mlsanity.com/paper/2103.01648/) (2021)
- [Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithms](https://mlsanity.com/paper/2103.10182/) (2021)
- [Variational Deep Image Restoration](https://mlsanity.com/paper/2207.01074/) (2022)
- [Basic Binary Convolution Unit for Binarized Image Restoration Network](https://mlsanity.com/paper/2210.00405/) (2022)
- [Stable Deep MRI Reconstruction using Generative Priors](https://mlsanity.com/paper/2210.13834/) (2022)

## Abstract (arXiv)

Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image restoration problems. By embodying recent improvements in nonlinear diffusion models, we propose a dynamic nonlinear reaction diffusion model with time-dependent parameters (ie, linear filters and influence functions). In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are simultaneously learned from training data through a loss based approach. We call this approach TNRD -- textitTrainable Nonlinear Reaction Diffusion. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for the tested applications. Our trained models preserve the structural simplicity of diffusion models and take only a small number of diffusion steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast.