Unfolding Generative Flows with Koopman Operators: Trajectory-Preserving Linearization 文章

arXiv:2506.22304v3 Announce Type: replace-cross Abstract: Continuous Normalizing Flows (CNFs) enable elegant generative modeling but remain bottlenecked by their iterative nature requiring costly sampling and lacking interpretability of the intermediate states. Recent approaches accelerate sampling by straightening trajectories or distilling endpoints, yet they treat the original generative process as a black box, discarding the teacher's intermediate dynamics. We propose a fundamentally different perspective: globally linearizing flow dynamics via Koopman theory to achieve trajectory-preserving linearization. By lifting a pre-trained Conditional Flow Matching (CFM) model into a higher-dimensional Koopman space, we represent its evolution with a single linear operator. Crucially, unlike boundary-only distillation, our method enforces infinitesimal consistency with the teacher's vector field along the full generative path.