Functional Mean Flow in Hilbert Space
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917084904030208 |
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| author | Li, Zhiqi Sun, Yuchen Turk, Greg Zhu, Bo |
| author_facet | Li, Zhiqi Sun, Yuchen Turk, Greg Zhu, Bo |
| contents | We present Functional Mean Flow (FMF) as a one-step generative model defined in infinite-dimensional Hilbert space. FMF extends the one-step Mean Flow framework to functional domains by providing a theoretical formulation for Functional Flow Matching and a practical implementation for efficient training and sampling. We also introduce an $x_1$-prediction variant that improves stability over the original $u$-prediction form. The resulting framework is a practical one-step Flow Matching method applicable to a wide range of functional data generation tasks such as time series, images, PDEs, and 3D geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional Mean Flow in Hilbert Space Li, Zhiqi Sun, Yuchen Turk, Greg Zhu, Bo Machine Learning Computer Vision and Pattern Recognition We present Functional Mean Flow (FMF) as a one-step generative model defined in infinite-dimensional Hilbert space. FMF extends the one-step Mean Flow framework to functional domains by providing a theoretical formulation for Functional Flow Matching and a practical implementation for efficient training and sampling. We also introduce an $x_1$-prediction variant that improves stability over the original $u$-prediction form. The resulting framework is a practical one-step Flow Matching method applicable to a wide range of functional data generation tasks such as time series, images, PDEs, and 3D geometry. |
| title | Functional Mean Flow in Hilbert Space |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2511.12898 |