# NeurOp-Diff:Continuous Remote Sensing Image Super-Resolution via Neural Operator Diffusion

arXiv: https://arxiv.org/abs/2501.09054 · HTML: https://mlsanity.com/paper/2501.09054/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 41 of its 57 references that are in the map.
- First posted on arXiv 15 Jan 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Accelerating the Super-Resolution Convolutional Neural Network](https://mlsanity.com/paper/1608.00367/) (2016)
- [AID: A Benchmark Dataset for Performance Evaluation of Aerial Scene Classification](https://mlsanity.com/paper/1608.05167/) (2016)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [Deeply-Recursive Convolutional Network for Image Super-Resolution](https://mlsanity.com/paper/1511.04491/) (2015)

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

- [Frequency-Aware Vision Transformers for High-Fidelity Super-Resolution of Earth System Models](https://mlsanity.com/paper/2502.12427/) (2025)
- [Beyond Visual Fidelity: Benchmarking Super-Resolution Models for Large-Scale Remote Sensing Imagery via Downstream Task Integration](https://mlsanity.com/paper/2605.00310/) (2026)
- [Super-Resolving Unseen Hyperspectral Sensors at Any Scale via Spatial Operators](https://mlsanity.com/paper/2609.39926/) (2026)

## Abstract (arXiv)

Most publicly accessible remote sensing data suffer from low resolution, limiting their practical applications. To address this, we propose a diffusion model guided by neural operators for continuous remote sensing image super-resolution (NeurOp-Diff). Neural operators are used to learn resolution representations at arbitrary scales, encoding low-resolution (LR) images into high-dimensional features, which are then used as prior conditions to guide the diffusion model for denoising. This effectively addresses the artifacts and excessive smoothing issues present in existing super-resolution (SR) methods, enabling the generation of high-quality, continuous super-resolution images. Specifically, we adjust the super-resolution scale by a scaling factor s, allowing the model to adapt to different super-resolution magnifications. Furthermore, experiments on multiple datasets demonstrate the effectiveness of NeurOp-Diff. Our code is available at https://github.com/zerono000/NeurOp-Diff.