Kernel-Gradient Drifting Models

Fuente: arXiv
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Main Authors: Esteban-Casadevall, Maria, Carrasco-Pollo, Jorge, Welling, Max, van de Meent, Jan-Willem, Bekkers, Erik J., Eijkelboom, Floor
Format: Preprint
Published: 2026
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author Esteban-Casadevall, Maria
Carrasco-Pollo, Jorge
Welling, Max
van de Meent, Jan-Willem
Bekkers, Erik J.
Eijkelboom, Floor
author_facet Esteban-Casadevall, Maria
Carrasco-Pollo, Jorge
Welling, Max
van de Meent, Jan-Willem
Bekkers, Erik J.
Eijkelboom, Floor
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_10727
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Kernel-Gradient Drifting Models
Esteban-Casadevall, Maria
Carrasco-Pollo, Jorge
Welling, Max
van de Meent, Jan-Willem
Bekkers, Erik J.
Eijkelboom, Floor
Machine Learning
Differential Geometry
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.
title Kernel-Gradient Drifting Models
topic Machine Learning
Differential Geometry
url https://arxiv.org/abs/2605.10727