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

2026-07-13

AI Summary

Existing rectified flow models struggle to balance between velocity field and endpoint prediction parameterizations, which compromises both generation quality and training stability. This work proposes Self-Consistent Flow (SC-Flow), a method that jointly optimizes a single network’s predictions of local velocities and data endpoints through a lightweight consistency loss, without altering the backbone architecture. By enforcing trajectory-wise agreement between these two predictions, SC-Flow significantly enhances the straightness of generated paths and improves training stability. Empirical results on image generation tasks demonstrate clear superiority over standard rectified flow baselines, yielding higher-quality samples.

Abstract

In rectified-flow-based generative models, the neural network can be trained to predict two different targets, such as the instantaneous velocity or the data endpoint, to perform denoising. Although prior work shows that these parameterizations lead to different empirical behaviors, the mechanisms underlying their respective advantages remain to be underexplored, and how to combine them effectively is still unclear. In this work, we analyze how learning errors from different parameterizations affect the generation performance. We show that predicting the data endpoint has a clear training signal that stabilizes training, whereas predicting the velocity maintains stable sampling dynamics near the data manifold. Motivated by these insights, we propose Self-Consistent Flow (SC-Flow), a new method that unifies the benefits of both parameterizations. By employing a lightweight consistency loss, SC-Flow jointly trains a single network to predict both the local velocity and the data endpoint, and the consistency between the two predictions improves the model's performance. The method requires no major architectural changes and adds minimal computational overhead. Extensive experiments on image generation tasks demonstrate that SC-Flow substantially stabilizes optimization and improves the straightness of generation paths, leading to significant gains in generation quality over standard rectified-flow baselines.

Problem

• rectified flow
• velocity prediction
• endpoint prediction
• generative models
• parameterization

Innovation

• Self-Consistent Flow
• rectified flow
• velocity prediction
• endpoint prediction
• consistency loss