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.
| Subjects: | Machine Learning (cs.LG); Differential Geometry (math.DG) |
| Cite as: | arXiv:2605.10727 [cs.LG] |
| (or arXiv:2605.10727v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.10727 arXiv-issued DOI via DataCite (pending registration) |
From: Maria Esteban Miss [view email]
[v1]
Mon, 11 May 2026 15:33:21 UTC (15,923 KB)
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