Kernel-Gradient Drifting Models
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 smoothed 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. Code is available \href{https://github.com/jcarrascopollo/kgd_thesis}{here}.
Related
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- Gradient estimates for the Green kernel under spectral Ricci bounds, and the stable Bernstein theorem in ℝ⁴
- A functional central limit theorem for kernel gradient flow and infinitesimal gradient boosting
- Generalization Analysis of Distributed Kernel-based Robust Gradient Descent Algorithms
- Kernel representations of fractional gradient bilinear forms. Part I. Constant coefficients
BibTeX
@misc{estebancasadevall2026kernelgradient,
title = {{Kernel-Gradient Drifting Models}},
author = {Maria Esteban-Casadevall and Jorge Carrasco-Pollo and Max Welling and Jan-Willem van de Meent and Erik J. Bekkers and Floor Eijkelboom},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.10727},
eprint = {2605.10727},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.10727},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kernel-Gradient Drifting Models
AU - Maria Esteban-Casadevall
AU - Jorge Carrasco-Pollo
AU - Max Welling
AU - Jan-Willem van de Meent
AU - Erik J. Bekkers
AU - Floor Eijkelboom
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2605.10727
UR - https://arxiv.org/abs/2605.10727
AB - 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 smoothed 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. Code is available \href{https://github.com/jcarrascopollo/kgd_thesis}{here}.
ER -