High-Order Drifting Models

Drifting models enable efficient one-step generation by evolving the model distribution through a kernel-induced transport field during training. Existing drifting methods, however, typically use only the local field value at sampled anchors, ignoring the local response structure of the same field. This leaves local curvature and higher-order structural mismatch unused, limiting convergence and generation fidelity. To address this problem, we propose Higher-Order Drifting Models, which exploit the local response hierarchy of the original kernel transport field. We show that the response derivatives of the field form a hierarchy of local cumulants; for Gaussian kernels, these cumulants correspond to spatial derivatives of the smoothed log-density ratio, extending the score-matching interpretation of drifting to higher orders. We further show that, under a local linearization, the higher-order responses act as a spectral reweighting that enhances the effective damping of transition-region modes without altering the asymptotic high-frequency behavior of the kernel. The experiments show that these responses provide complementary optimization signals while preserving one-step inference, accelerating convergence and improving generation accuracy, with diminishing returns as the order increases.