Multi-Temporal Mean-Reverting SDE with Preconditioned Diffusion for Remote Sensing Cloud Removal

Remote sensing (RS) imagery is frequently compromised by environmental factors like cloud cover, leading to severe information loss and hindering downstream Earth observation tasks. Although generative paradigms like Diffusion Models and Stochastic Differential Equations (SDEs) show promise in image restoration, they encounter critical bottlenecks in multi-temporal RS scenarios: 1) failing to fully exploit spatio-temporal redundancies and cross-modal complementarities; and 2) suffering from unstable convergence in heavy-cloud regions due to drastic variance in noise levels. To address these challenges, we propose a Preconditioned Mean-Reverting SDE (PMR-SDE) framework for multi-temporal cloud removal. Moving beyond standard generative adaptations, we reformulate the restoration task as a cross-modally conditioned mean-reverting process, which characterizes the continuous evolution from a cloud-distorted state toward a clear reference, explicitly guided by Sentinel-1 SAR features acting as a physical structural anchor. Within this framework, a Spatio-Temporal Dual-Branch Attention (ST-DBA) module is developed to capture long-range optical dependencies while bridging the semantic modality gap. Furthermore, we introduce an Instance-Adaptive Preconditioning Control strategy to rescale the input-output dynamics of the denoiser based on dynamic local priors, effectively alleviating fitting pressures and enhancing gradient stability during extreme diffusion stages. Extensive experiments on the SEN12MS-CR-TS dataset demonstrate that our method achieves strong spatial texture reconstruction and structural fidelity, with competitive performance under heavy-cloud scenarios while maintaining favorable spectral preservation.