Kernel-Gradient Drifting Models

TL;DR

This paper introduces kernel-gradient drifting, a flexible generative modeling framework that generalizes drifting models using kernel-induced directions, enabling high-quality one-step generation across various data types.

Contribution

It extends drifting models to general kernels and manifolds, providing a unified, score-based interpretation and demonstrating state-of-the-art results in diverse applications.

Findings

Achieves state-of-the-art one-step generation on spherical geospatial data.

Extends drifting models to Riemannian manifolds and discrete data.

Provides a score-based interpretation for general kernels.

Abstract

We propose kernel-gradient drifting, a one-step generative modeling framework that replaces the fixed Euclidean displacement direction in drifting models with directions induced by the kernel itself. Standard drifting is attractive because it enables fast, high-quality generation without distilling a large pretrained diffusion model, but its theory is currently understood mainly for Gaussian kernels, where the drift coincides with smoothed score matching and is identifiable. Our gradient-based reformulation exposes this score-based structure for general kernels: the resulting drift is the score difference between kernel-smoothed data and model distributions, yielding identifiability for characteristic kernels and a smoothed-KL descent interpretation of the drifting dynamics. Since kernel gradients are intrinsic tangent vectors, the same construction extends naturally to Riemannian manifolds and to discrete data via the Fisher-Rao geometry of the probability simplex. Across spherical geospatial data, promoter DNA and molecule generation, kernel-gradient drifting enables state-of-the-art one-step generation beyond the Euclidean setting without distillation.