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arXiv · 2511.12898

Functional Mean Flow in Hilbert Space

Zhiqi Li·Yuchen Sun·Greg Turk·Bo Zhu
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Abstract

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.

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Zhiqi Li, Yuchen Sun, Greg Turk, Bo Zhu. 2025-11-17. Functional Mean Flow in Hilbert Space. https://arxiv.org/abs/2511.12898

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