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arXiv · 2602.01988

Stochastic Interpolants in Hilbert Spaces

James Boran Yu·RuiKang OuYang·Julien Horwood·José Miguel Hernández-Lobato
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Abstract

Although diffusion models have successfully extended to function-valued data, stochastic interpolants -- which offer a flexible way to bridge arbitrary distributions -- remain limited to finite-dimensional settings. This work bridges this gap by establishing a rigorous framework for stochastic interpolants in infinite-dimensional Hilbert spaces. We provide comprehensive theoretical foundations, including proofs of well-posedness and explicit error bounds. We demonstrate the effectiveness of the proposed framework for conditional generation, focusing particularly on complex PDE-based benchmarks. By enabling generative bridges between arbitrary functional distributions, our approach achieves state-of-the-art results, offering a powerful, general-purpose tool for scientific discovery.

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James Boran Yu, RuiKang OuYang, Julien Horwood, José Miguel Hernández-Lobato. 2026-02-02. Stochastic Interpolants in Hilbert Spaces. https://arxiv.org/abs/2602.01988

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