Stochastic Interpolants in Hilbert Spaces

• URL: http://arxiv.org/abs/2602.01988v1
• Date: Mon, 02 Feb 2026 11:44:34 GMT
• Title: Stochastic Interpolants in Hilbert Spaces
• Authors: James Boran Yu, RuiKang OuYang, Julien Horwood, José Miguel Hernández-Lobato,
• Abstract summary: interpolants offer a flexible way to bridge arbitrary distributions.<n>This paper establishes a rigorous framework for Hilbert interpolants in infinite-dimensional spaces.<n>We demonstrate the effectiveness of the proposed framework for conditional generation.
• Score: 22.77471216660321
• License: http://creativecommons.org/licenses/by/4.0/
• 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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