From Navigation to Refinement: Revealing the Two-Stage Nature of Flow-based Diffusion Models through Oracle Velocity

arXiv:2512.02826v3 Announce Type: replace-cross Abstract: Flow-based diffusion models have emerged as a leading paradigm for training generative models across images and videos. However, their memorization-generalization behavior remains poorly understood. In this work, we revisit the flow matching (FM) objective and study its marginal velocity field, which admits a closed-form expression, allowing exact computation of the oracle FM target. Analyzing this oracle velocity field reveals that flow-