# Progressive Image Super-Resolution via Neural Differential Equation

arXiv: https://arxiv.org/abs/2101.08987 · HTML: https://mlsanity.com/paper/2101.08987/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 22 Jan 2021.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [Toward Real-World Single Image Super-Resolution: A New Benchmark and A New Model](https://mlsanity.com/paper/1904.00523/) (2019)
- [Deeply-Recursive Convolutional Network for Image Super-Resolution](https://mlsanity.com/paper/1511.04491/) (2015)
- [Deep Back-Projection Networks For Super-Resolution](https://mlsanity.com/paper/1803.02735/) (2018)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)

## Abstract (arXiv)

We propose a new approach for the image super-resolution (SR) task that progressively restores a high-resolution (HR) image from an input low-resolution (LR) image on the basis of a neural ordinary differential equation. In particular, we newly formulate the SR problem as an initial value problem, where the initial value is the input LR image. Unlike conventional progressive SR methods that perform gradual updates using straightforward iterative mechanisms, our SR process is formulated in a concrete manner based on explicit modeling with a much clearer understanding. Our method can be easily implemented using conventional neural networks for image restoration. Moreover, the proposed method can super-resolve an image with arbitrary scale factors on continuous domain, and achieves superior SR performance over state-of-the-art SR methods.