FM-ChangeNet++: Learned Nonlinear Feature Transport for Change Detection

Most remote sensing change detection methods infer change by directly comparing features extracted from bi-temporal images. Recent flow-matching approaches reinterpret this problem as learning feature transport between pre- and post-temporal representations through a fixed linear interpolation path. While effective, this assumption constrains semantic transitions to follow straight trajectories in feature space, limiting the representation of complex structural changes. We introduce FM-ChangeNet++, a feature transport framework that learns the transformation trajectory itself. Instead of enforcing a fixed linear path, we model feature evolution using an endpoint-preserving residual transport formulation, where a lightweight residual predictor learns smooth nonlinear deviations while guaranteeing that the trajectory starts from the pre-temporal representation and terminates at the post-temporal representation. The velocity field is supervised using the instantaneous derivative of the learned nonlinear path, ensuring that the predicted velocity represents the local tangent direction and transport intensity along the feature trajectory. Its magnitude therefore provides a localized measure of feature evolution that can support semantic change detection. The proposed framework jointly optimizes multi-scale flow estimation, residual path regularization, spatial smoothness, and segmentation supervision within a unified coarse-to-fine architecture. This formulation enables the model to capture complex feature evolution while maintaining endpoint consistency and controlled transport dynamics. Extensive experiments on standard remote sensing benchmarks demonstrate consistent improvements over linear transport formulations and state-of-the-art CD methods. Ablation studies further show that learned residual transport produces more discriminative feature trajectories, more localized velocity representations, and more accurate detection of subtle semantic changes.