Space-FreqDiffSR: a spatial–frequency coupled diffusion model for high-fidelity super-resolution of remote-sensing images

To address the challenge of disentangling spatial-domain structures and frequency-domain spectral characteristics in existing models, we propose Space Frequency Coupled Difference Super-Resolution (Space-FreqDiff SR). The proposed framework adopts a dual-branch collaborative architecture. Specifically, the Spatial Reconstruction Encoding Module (SREM) is designed to capture global geometric structures and layout information in the spatial domain, while the Frequency Reconstruction Enhancement Module (FREM) focuses on extracting and enhancing cross-band texture details by integrating multi-scale Fast Fourier Transform (FFT) operations with adaptive high-pass filtering. Subsequently, the Scene-Adaptive Gating Fusion (SGF) module performs cross-domain attention alignment and dynamic feature weighting, generating scene-aware frequency enhancement representations. The resulting dual-domain conditional vectors are then progressively injected into the Frequency-Token Reinforced Multi-scale Transformer Network (FTRM-Net). This design enables consistent structural constraints and texture guidance across different diffusion scales, thereby achieving precise spectral routing throughout the super-resolution process. Experimental results demonstrate that, for 4× super-resolution on the AID and WHU-RS19 benchmark datasets, Space-FreqDiff SR achieves PSNR/SSIM values of 31.77 dB/0.8321 and 30.18 dB/0.7915, respectively, outperforming state-of-the-art methods such as IRR-DiffSR. In no-reference evaluations using real Sentinel-2 and GF-2 imagery, the proposed method consistently surpasses competing approaches across perceptual quality metrics, including NIQE and PIQE. Furthermore, the NDVI and NDWI values derived from the reconstructed images closely match those of high-resolution references, indicating strong spectral fidelity. Overall, Space-FreqDiff SR demonstrates superior performance in structural reconstruction, frequency-domain detail enhancement, and spectral consistency, highlighting its high accuracy and strong potential for practical remote sensing applications.