Gradient Flow Drifting: One-Step Generative Modeling with KDE Divergence Flows

We introduce Gradient Flow Drifting(GFD), a unified, directly estimable energy-defined framework for one-step implicit generative modeling. GFD treats state-space geometry, kernel representation, and divergence energy as explicit modeling choices and maps them to particle dynamics and generator training through a common variational construction. The central principle is to take the Wasserstein gradient of the KDE-defined energy with respect to the clean model distribution and amortize the resulting particle updates into a neural generator. For admissible kernel-density $f$-divergences, we derive the first variation, clean-particle fields, energy dissipation along classical flows, and distributional identification under injective smoothing. The framework also incorporates a quadratic distance between kernel densities as a density-ratio-free energy and supports nonnegative energy mixtures through the corresponding linear combination of particle fields. Gaussian and von Mises-Fisher kernels give explicit Euclidean and spherical instances. Sample-based field estimation and stop-gradient regression provide a common training procedure while preserving single-pass inference. Experiments on encoder-free synthetic distributions, spherical directional data, and high-dimensional DNA sequences, alongside encoder-based CIFAR-10 and ImageNet-256 generation, demonstrate the effectiveness and versatility of representative GFD instances and analyze the behavior of different divergence choices.