DirectSR: Rethinking Zero-Origin Residual Flow via Observation-Guided Endpoint Prediction for Remote Sensing Super-Resolution

Remote sensing super-resolution requires both fine-detail recovery and strict spatial consistency with the observed scene. We revisit a zero-origin deterministic residual flow with target $R=x_{HR}-B$ and linear path $x_t=tR$, for which the analytical velocity target remains constant and equal to R along the trajectory. This motivates direct endpoint recovery without explicit time-dependent residual transport. We propose DirectSR, which predicts the target residual through a single endpoint-predictor evaluation, conditioned on frozen multi-scale DINOv2 features, pixel-aligned differential responses, and an LR-consistency correction. We further study an optional candidate-aware refinement stage, DirectSR+. On Potsdam and Toronto 2×, DirectSR improves over a matched four-step residual flow by 2.4442 and 3.2632 dB, respectively. Under our unified evaluation protocol, DirectSR achieves the best PSNR and SSIM on Toronto 4× and ranks first on all reported structural metrics, while DirectSR+ achieves the best PSNR and SSIM on Potsdam and Toronto 2×. Final-candidate experiments further show that Stage-2 refinement is dataset dependent, supporting DirectSR Stage-1 as the default model. These results support direct endpoint recovery as a simpler alternative to iterative integration in the deterministic paired residual formulation studied here, without extending this conclusion to stochastic flow, diffusion, or multimodal generative models.