Constant Acceleration Flow

Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows under the assumption that image and noise pairs, known as coupling, can be approximated by straight trajectories with constant velocity. However, we observe that the constant velocity modeling and reflow procedures have limitations in accurately learning to couple with flow crossing, leading to suboptimal few-step generation. To overcome the limitations, we introduce the Constant Acceleration Flow (CAF), a novel framework based on a simple constant acceleration equation. Additionally, we propose two techniques to improve estimation accuracy: initial velocity conditioning for the acceleration model and a reflow process for the initial velocity. Our comparative studies show that CAF not only outperforms rectified flow with reflow procedures in terms of speed and accuracy but also demonstrates substantial improvements in preserving coupling for fast generation.