Learning goal: the conditional reference paths are straight lines, but their conditional mean field can vary along generated trajectories. Coarse Euler steps can miss that variation.

Thin green: conditional reference lines; thick indigo/gold: generated marginal ODE paths; blue: source; orange: target.

Pairing rule
Display
Euler steps
Path length / endpoint distance = — Endpoint error at this step count = —

Choose “ Position-based pairing ”: this toy's aligned pairing reduces crossings and gives nearly straight, near-constant-speed generated paths, so a few Euler steps can work well. Random pairing changes the conditional averages and introduces more velocity variation. Straight reference lines alone do not guarantee straight generated paths. Both pairings retain the same source and target clouds; only their joint pairing changes.