# Implicit Euler ODE Networks for Single-Image Dehazing

arXiv: https://arxiv.org/abs/2007.06443 · HTML: https://mlsanity.com/paper/2007.06443/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2020.

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

- [An Efficient Domain-Incremental Learning Approach to Drive in All Weather Conditions](https://mlsanity.com/paper/2204.08817/) (2022)
- [MetaNODE: Prototype Optimization as a Neural ODE for Few-Shot Learning](https://mlsanity.com/paper/2103.14341/) (2021)
- [IM-BERT: Enhancing Robustness of BERT through the Implicit Euler Method](https://mlsanity.com/paper/2505.06889/) (2025)
- [Stability of implicit neural networks for long-term forecasting in dynamical systems](https://mlsanity.com/paper/2305.17155/) (2023)
- [IIET: Efficient Numerical Transformer via Implicit Iterative Euler Method](https://mlsanity.com/paper/2509.22463/) (2025)
- [PiGRAND: Physics-informed Graph Neural Diffusion for Intelligent Additive Manufacturing](https://mlsanity.com/paper/2603.15194/) (2026)

## Abstract (arXiv)

Deep convolutional neural networks (CNN) have been applied for image dehazing tasks, where the residual network (ResNet) is often adopted as the basic component to avoid the vanishing gradient problem. Recently, many works indicate that the ResNet can be considered as the explicit Euler forward approximation of an ordinary differential equation (ODE). In this paper, we extend the explicit forward approximation to the implicit backward counterpart, which can be realized via a recursive neural network, named IM-block. Given that, we propose an efficient end-to-end multi-level implicit network (MI-Net) for the single image dehazing problem. Moreover, multi-level fusing (MLF) mechanism and residual channel attention block (RCA-block) are adopted to boost performance of our network. Experiments on several dehazing benchmark datasets demonstrate that our method outperforms existing methods and achieves the state-of-the-art performance.