Unfolding Generative Flows with Koopman Operators: Fast and Interpretable Sampling

Continuous Normalizing Flows (CNFs) offer elegant generative modeling but remain slow to sample from, as each sample requires solving a nonlinear ODE.
This paper proposes a Koopman operator–based linearization of flow dynamics, allowing one-step analytical sampling and spectral interpretability.

By lifting Conditional Flow Matching into a higher-dimensional Koopman space, we represent its evolution via a single linear operator.
This makes sampling fully parallelizable and provides an interpretable spectral structure of the generation process.

We derive a simulation-free training objective enforcing infinitesimal consistency with the teacher model and demonstrate:

• Competitive generative quality with large speedups
• Consistency-trained models that reveal disentangled Koopman modes
• New interpretability of flow dynamics via eigen-decomposition

[arXiv]

Recommended citation: Erkan Turan, Ari Siozopoulos, Louis Martinez, Julien Gaubil, Emery Pierson, and Maks Ovsjanikov. (2025). *Unfolding Generative Flows with Koopman Operators: Fast and Interpretable Sampling.* Preprint, under review.
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