Rethinking Where Robot Actions Begin: Learning an Expert-Inversion Prior

Flow-matching robot policies have demonstrated strong performance, yet typically sample starting points from a fixed Gaussian prior without explicitly leveraging source information from expert demonstrations. We find that expert-inverted source distributions can deviate from this prior even with numerically accurate inversion, and that source–observation correspondence affects generated actions. Our theoretical analysis establishes that, under ideal invertibility, matching the expert conditional source distribution is equivalent to matching the expert conditional action distribution. These findings motivate Expert-Inversion Prior Flow, a two-stage framework in which a conditional prior flow learns to transport Gaussian noise to observation-matched sources, while a frozen action flow decodes these sources into action sequences. Systematic experiments demonstrate improved agreement with expert actions over unconditional source modeling, supporting the value of observation-conditioned expert-source learning for inference-time guidance.