Title: Implicit Dynamical Flow Fusion for generative modeling
Primary area: generative models
Keywords: Time Series Generation, Conditional Flow Matching, High-Order Dynamics, Molecular Simulation, Sea Surface Temperature

Abstract: Conditional Flow Matching (CFM) models can generate high-quality samples from a non-informative prior, but can require hundreds of network evaluations (NFE), making them computationally expensive. To address this limitation, we introduce Implicit Dynamical Flow Fusion (IDFF), which augments CFM's vector field with learnable momentum terms derived from higher-order derivatives of the log-density. These momentum terms provide geometric information about the probability landscape, enabling more efficient transport from noise to data while preserving the marginal distributions through compensating diffusion. As a result, IDFF reduces the NFEs by a factor of ten compared to CFMs without significantly sacrificing sample quality, allowing for rapid sampling and efficient handling of time-series data generation tasks with compatibility with any ODE solver. We evaluate IDFF on benchmarks for time series and image generation. IDFF demonstrates superior performance on time-series datasets, including molecular dynamics simulation and sea surface temperature (SST) forecasting, highlighting its versatility and effectiveness across diverse domains. For image generation, IDFF achieved an FID score of 2.78 on CIFAR-10, outperforming all existing CFM variants in efficiency while requiring only 10 NFEs compared to 100+ for standard methods.