Coupling Trajectory Rectification and Perceptual Supervision in Rectified Flow

Rectified Flow straightens the trajectories of a flow model so that they can be integrated accurately with few steps, but it supervises the velocity along each path rather than the resulting image. Another family of few-step methods instead supervises that image directly against a teacher, often under a perceptual distance, and reaches high quality at small budgets, but usually trains each model for a fixed number of steps. We propose RefineFlow, which unites both forms of supervision in a single prediction. This prediction, the endpoint estimated by the model, is matched to the teacher's image under a perceptual distance and simultaneously defines the rectification target. Supervision on the output thereby shapes the velocity field along the whole trajectory and straightens it, within a reflow stage and without extra network evaluation or teacher integration. On text-to-image backbones, RefineFlow improves few-step generation quality and prompt alignment over the corresponding reflow baselines with far fewer trainable parameters, without training a separate model for each number of steps.