Generative Modeling via Kernelized Stochastic Interpolants

arXiv:2602.20070v3 Announce Type: replace 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) = nablaphi(x)^opeta_t, where eta_t in R^P solves a Pimes 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 generation and model combination without neural network training. We demonstrate the approach on financial time series, turbulence, and image generation.

Source: arXiv cs.LG | 2026-06-23