Stochastic Interpolants in Hilbert Spaces
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912868359733248 |
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| author | Yu, James Boran OuYang, RuiKang Horwood, Julien Hernández-Lobato, José Miguel |
| author_facet | Yu, James Boran OuYang, RuiKang Horwood, Julien Hernández-Lobato, José Miguel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01988 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Interpolants in Hilbert Spaces Yu, James Boran OuYang, RuiKang Horwood, Julien Hernández-Lobato, José Miguel Machine Learning 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. |
| title | Stochastic Interpolants in Hilbert Spaces |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.01988 |