The offline dataset only stores the final action x^F (drag the teal dot) — never the intermediate denoise steps. But because the flow is deterministic, we can integrate the velocity field backwards from x^F to recover the whole path x^F→…→x⁰ (blue) for free. That reconstructed "virtual trajectory" is on-policy and noise-free, which is exactly what the extended framework needs. Drag x^F anywhere; the reversal follows.