{"ID":2840306,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.12898","arxiv_id":"2511.12898","title":"Functional Mean Flow in Hilbert Space","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.","short_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. W...","url_abs":"https://arxiv.org/abs/2511.12898","url_pdf":"https://arxiv.org/pdf/2511.12898v1","authors":"[\"Zhiqi Li\",\"Yuchen Sun\",\"Greg Turk\",\"Bo Zhu\"]","published":"2025-11-17T02:38:28Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CV\"]","methods":"[]","has_code":false}