Kernel-Gradient Drifting Models
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910209425801216 |
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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 |