Training-Free Generative Modeling via Kernelized Stochastic Interpolants

• URL: http://arxiv.org/abs/2602.20070v2
• Date: Wed, 25 Feb 2026 16:39:12 GMT
• Title: Training-Free Generative Modeling via Kernelized Stochastic Interpolants
• Authors: Florentin Coeurdoux, Etienne Lempereur, Nathanaël Cuvelle-Magar, Thomas Eboli, Stéphane Mallat, Anastasia Borovykh, Eric Vanden-Eijnden,
• Abstract summary: We develop a kernel method for generative modeling within the interpolant framework.<n>We demonstrate the approach on financial time series, turbulence, and image generation.
• Score: 20.24989080858456
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a kernel method for generative modeling within the stochastic interpolant framework, replacing neural network training with linear systems. The drift of the generative SDE is $\hat b_t(x) = \nablaφ(x)^\topη_t$, where $η_t\in\R^P$ solves a $P\times P$ system computable from data, with $P$ independent of the data dimension $d$. Since estimates are inexact, the diffusion coefficient $D_t$ affects sample quality; the optimal $D_t^*$ from Girsanov diverges at $t=0$, but this poses no difficulty and we develop an integrator that handles it seamlessly. The framework accommodates diverse feature maps -- scattering transforms, pretrained generative models etc. -- enabling training-free generation and model combination. We demonstrate the approach on financial time series, turbulence, and image generation.

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