Generative Modeling via Kernelized Stochastic Interpolants

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 bt(x) = nablaφ(x)^topηt, where ηt ∈ ℝP solves a P× P system computable from data, with P independent of the data dimension d. Since estimates are inexact, the diffusion coefficient Dt affects sample quality; the optimal Dt^* 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.