Condition-Once Flow Matching for Conditional Multivariate Tabular Generation

Tabular data often pair observed covariates with multiple continuous responses whose joint distribution matters beyond a point prediction. We study conditional multivariate tabular generation, where covariates remain fixed while a designated response block is generated jointly, preserving conditional location, uncertainty, and cross-response dependence. Conventional conditional flow models repeatedly supply the same context to the velocity throughout transport. With a learnable conditional source, however, context information can already be encoded into the evolving state, leaving open how much direct velocity conditioning remains useful. We characterize this residual predictive value and show that it vanishes as the state becomes sufficient for velocity prediction, yielding condition saturation. Guided by this result, we introduce Condition-Once Flow Matching (CoFM), which uses a learnable conditional source and a velocity shared across contexts, together with Conditional Source Forcing (CS-Forcing) to control local source expansion over heterogeneous tabular fields. Controlled studies support the predicted saturation behavior. Across four real-world benchmarks covering Beijing air quality, Superconductivity, GTEx, and UK Biobank proteomics, CoFM-CSF consistently surpasses ten competitive probabilistic and generative baselines in overall predictive and distributional performance.