# WaveDiffUR: A diffusion SDE-based solver for ultra magnification super-resolution in remote sensing images

arXiv: https://arxiv.org/abs/2412.18996 · HTML: https://mlsanity.com/paper/2412.18996/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 58 references that are in the map.
- First posted on arXiv 25 Dec 2024.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)

## Built on by (most cited first, 1 of 1)

- [Diffusion Models for Hyperspectral Image Analysis: A Comprehensive Review](https://mlsanity.com/paper/2505.11158/) (2025)

## Abstract (arXiv)

Deep neural networks have recently achieved significant advancements in remote sensing superresolu-tion (SR). However, most existing methods are limited to low magnification rates (e.g., 2 or 4) due to the escalating ill-posedness at higher magnification scales. To tackle this challenge, we redefine high-magnification SR as the ultra-resolution (UR) problem, reframing it as solving a conditional diffusion stochastic differential equation (SDE). In this context, we propose WaveDiffUR, a novel wavelet-domain diffusion UR solver that decomposes the UR process into sequential sub-processes addressing conditional wavelet components. WaveDiffUR iteratively reconstructs low-frequency wavelet details (ensuring global consistency) and high-frequency components (enhancing local fidelity) by incorporating pre-trained SR models as plug-and-play modules. This modularity mitigates the ill-posedness of the SDE and ensures scalability across diverse applications. To address limitations in fixed boundary conditions at extreme magnifications, we introduce the cross-scale pyramid (CSP) constraint, a dynamic and adaptive framework that guides WaveDiffUR in generating fine-grained wavelet details, ensuring consistent and high-fidelity outputs even at extreme magnification rates.