Learning goal: there are many maps G transporting N(0,I) to p_data. Changing the pairing leaves both endpoint clouds unchanged while changing which points are paired and the reference interpolation between them.

Pale blue: N(0,I) samples · Pale orange: p _data samples · Solid: current x at time _t Thin lines: chosen reference paths

Pause at an intermediate time, then change the pairing: the endpoint clouds stay fixed while the intermediate x cloud _t and reference paths change.