WaveDiffUR: A Wavelet-Domain Diffusion Model for Ultraresolution in Remote Sensing

Deep learning (DL) has significantly advanced super-resolution (SR), a technique that enhances low-quality images by reconstructing fine details. However, most DL-based SR methods struggle at high magnification levels (e.g., ×4 or higher) due to dramatically increased ill-posedness. To overcome this, we define high-magnification SR as an ultra-resolution (UR) problem and introduce WaveDiffUR, a novel wavelet-domain diffusion model designed for extreme-scale image reconstruction. WaveDiffUR decomposes the UR process into sequential steps, first restoring low-frequency wavelet details for global consistency and then refining high-frequency components for sharper textures. By integrating pre-trained SR models as modular components, it reduces ill-posedness and ensures adaptability across different applications. Unlike existing SR approaches, which struggle with fixed boundary conditions at extreme magnifications, WaveDiffUR incorporates the cross-scale pyramid (CSP) constraint, an adaptive framework that dynamically refines low- and high-frequency wavelet details to maintain consistency and high fidelity. Extensive experiments demonstrate that WaveDiffUR with CSP notably enhances spatial accuracy and consistently generates high-frequency details with remarkable fidelity during the SR process. Evaluations are conducted across two benchmark evaluation datasets and four additional independent datasets. The empirical results reveal that, as magnification scales from ×8 to ×128, WaveDiffUR achieves an average degradation rate in PSNR, NIQE, and SRE of only 19.1%—the best performance among all benchmarked models—while consistently delivering sharper images characterized by superior spatial fidelity. By enabling scalable, high-fidelity ultra-resolution, WaveDiffUR opens new possibilities for remote sensing applications, including environmental monitoring, urban planning, disaster response, and precision agriculture.