Implicit Dynamical Flow Fusion (IDFF) for Generative Modeling

TMLR Paper9493 Authors

Abstract: Conditional Flow Matching (CFM) generates high-quality samples by learning a deterministic transport from noise to data, but typically requires over a hundred network function evaluations (NFEs) per sample, especially in time-series settings. We introduce Implicit Dynamical Flow Fusion (IDFF), which augments the CFM vector field with learnable momentum terms derived from higher-order derivatives of the log-density. IDFF comes with two clearly separated theoretical guarantees. At first order, with our default Langevin-enhanced schedule, IDFF preserves the CFM marginal density exactly in continuous time. At higher orders, a single Girsanov-to-Pinsker argument bounds the endpoint deviation by a closed-form expression that depends only on the weighted score-matching loss our training objective already minimizes; consequently, the endpoint deviation vanishes as the number of NFEs grows. The practical enabler behind both regimes is a re-parameterization identity: every higher-order marginal derivative can be obtained from the learned first-order score by automatic differentiation, so no additional networks are trained. Empirically, IDFF reduces NFEs by an order of magnitude with no loss in sample quality. On CIFAR-10 it achieves an FID of 2.78 at 10 NFEs, outperforming existing CFM variants and matching methods that need over a hundred evaluations. For time-series modelling, IDFF performs strongly on molecular-dynamics simulation and sea-surface-temperature forecasting at a fraction of the compute. Overall, momentum-augmented flows offer a principled and efficient route to generative modelling across both static and dynamic domains.

Submission Type: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Mathurin_Massias1

Submission Number: 9493