Linearized Coupling Flow with Shortcut Constraints for One-Step Face Restoration

Face restoration can be formulated as a continuous-time transformation between image distributions via Flow Matching (FM). However, standard FM typically employs independent coupling, ignoring the statistical correlation between low-quality (LQ) and high-quality (HQ) data. This leads to intersecting trajectories and high velocity-field curvature, requiring multi-step integration. We propose Shortcut-constrained Coupling Flow for Face Restoration (SCFlowFR) to address these challenges. By establishing a data-dependent coupling, we explicitly model the LQ-HQ dependency to minimize path crossovers and promote near-linear probability flow. Furthermore, we employ a conditional mean estimator to refine the source distribution's anchor, effectively tightening the transport cost and stabilizing the velocity field. To ensure stable one-step inference, a shortcut constraint is introduced to supervise average velocities over arbitrary intervals, mitigating discretization bias in large-step updates. SCFlowFR achieves state-of-the-art one-step restoration, providing a superior trade-off between perceptual fidelity and computational efficiency.