Enhancing the straightness of the flow trajectory.

[levon-khachatryan]

Hi!

First of all, congrats on your great work, and thank you for open-sourcing it! Can you explain in more detail why equations 9 and 10 from the paper should enhance the straightness of the flow trajectory?

Thanks in advance.

[feifeiobama]

The straightness of the flow trajectory is usually compromised when there are intersections. Sampling the endpoints independently (as in vanilla flow matching) creates random directions for each trajectory and leads to intersections. Instead, by coupling the sampling of these endpoints (as in Equations 9 and 10), we can create more organized, possibly parallel trajectories with fewer intersections, thus improving straightness.

[levon-khachatryan]

Thanks for the answer.