Training-Free Generative Modeling via Kernelized Stochastic Interpolants

TL;DR

This paper introduces a kernel-based, training-free generative modeling method that replaces neural networks with linear systems, enabling efficient data generation across various domains without extensive training.

Contribution

It presents a novel kernel method within the stochastic interpolant framework that replaces neural network training with linear systems, adaptable to diverse feature maps.

Findings

Effective generation on financial time series

Successful turbulence data modeling

High-quality image generation results

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 $\hat b_t(x) = \nabla\phi(x)^\top\eta_t$, where $\eta_t\in\R^P$ 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.