Self-Consistent Flow: Unifying Velocity and Endpoint Prediction for Rectified Flow Models

This paper studies why velocity prediction and data-endpoint prediction behave differently in rectified-flow generative models. It argues that endpoint prediction provides a clearer training signal that stabilizes optimization, while velocity prediction supports more stable sampling near the data manifold. The proposed Self-Consistent Flow (SC-Flow) trains one network to predict both quantities and adds a lightweight consistency loss linking them. According to the abstract, image-generation experiments show improved optimization stability, straighter generation paths, and better quality than standard rectified-flow baselines, with minimal computational overhead and no major architectural changes.