Functional Mean Flow in Hilbert Space

Zhiqi Li, Yuchen Sun, Greg Turk, Bo Zhu; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2026, pp. 1928-1938

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.

Related Material

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[bibtex]
@InProceedings{Li_2026_CVPR, author = {Li, Zhiqi and Sun, Yuchen and Turk, Greg and Zhu, Bo}, title = {Functional Mean Flow in Hilbert Space}, booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}, month = {June}, year = {2026}, pages = {1928-1938} }