# Smooth Flow Matching for Synthesizing Functional Data Source: [Smooth Flow Matching for Synthesizing Functional Data]() Collection index: [llms.txt]() Data updated: 2026-08-13T05:00:05.216Z Authors: Jianbin Tan, Anru R. Zhang Published: 2025-08-19T13:50:23.000Z ## Abstract Functional data, i.e., random functions observed over a continuous domain, are increasingly available in areas such as biomedical research, health informatics, and epidemiology. However, effective statistical analysis for functional data is often hindered by challenges such as privacy constraints, sparse and irregular sampling, infinite-dimensionality, and non-Gaussian structures. To address these challenges, we introduce a novel framework named Smooth Flow Matching (SFM), tailored for generative modeling of functional data that enables statistical analysis without exposing sensitive real data. Under a copula framework, SFM constructs a semiparametric smooth flow to generate infinite-dimensional functional data, free of Gaussianity and low-rank assumptions. It is computationally efficient, handles irregular observations, and guarantees the smoothness of the generated functions, offering a practical and flexible solution in scenarios where existing deep generative methods are not applicable. Through extensive simulation studies, we demonstrate the advantages of SFM in terms of both synthetic data quality and computational efficiency. We then apply SFM to generate clinical trajectory data from the MIMIC-IV patient electronic health records (EHR) longitudinal database. Our analysis showcases the ability of SFM to produce high-quality surrogate data for downstream tasks, highlighting its potential to boost the utility of EHR data for clinical applications. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Functional Property Estimation on Synthetic Gamma Process Scenario B (sparsity {2, ..., 6})](): Functional Property Estimation; Synthetic Gamma Process Scenario B, sparsity {2, ..., 6}; MSE (MF): 0.1. - [Functional Property Estimation on Synthetic Gamma Process Scenario B (sparsity {6, ..., 10})](): Functional Property Estimation; Synthetic Gamma Process Scenario B, sparsity {6, ..., 10}; MSE (MF): 0.08. ## Original sources and implementation [Original paper]() [PDF]()