DualCDM: Dual-domain conditional diffusion for SAR-to-optical translation with spatial–frequency correlation and adaptive feature recalibration

Translating Synthetic aperture radar (SAR) images into optical images is intrinsically ill-posed because microwave backscatter and optical reflectance describe different physical properties of the observed scene. Although frequency-domain modeling has been introduced into diffusion-based translation, existing methods mainly rely on independent weighting of individual Fourier coefficients and provide limited modeling of interactions among neighboring frequencies and feature channels. To address this limitation, we propose dualCDM, a conditional diffusion model that jointly exploits spatial- and frequency-domain representations. In the diffusion backbone, a spatial-frequency hybrid residual block (SFHRB) combines a spatial convolution branch with complex-valued convolution in the Fourier domain. The complex convolution aggregates neighboring Fourier coefficients across all input feature channels, enabling local cross-frequency and cross-channel modeling, while its response is modulated by the diffusion timestep. In the SAR conditional encoder, an adaptive frequency-domain feature recalibration block (AFFRB) predicts input-dependent real-valued gains from magnitude and trigonometric phase representations of intermediate GRD features. These gains adaptively recalibrate the complex frequency responses without introducing an additional phase shift, while the residual connection preserves the original conditional information. A dual-domain objective further constrains both the predicted diffusion noise and the one-step optical reconstruction in the spatial and frequency domains. We also construct the S1S2 dataset using 16-bit Sentinel-2 reflectance data, retaining the original 0–10,000 value range and including the near-infrared band. Experiments on SEN1-2 and S1S2 show that dualCDM improves radiometric accuracy, spectral consistency, and structural preservation over six representative methods. Paired statistical tests further confirm significant improvements over the strongest competing method across all six evaluation metrics on both datasets.