CONSTRUCT-FIRST FLOW MATCHING FOR FEW-PASS TIME-SERIES GENERATION

Short-window time-series generation requires reproducing both temporal depen- dence and non-Gaussian structure, some of which can be estimated directly from training data. How much learned dynamics remain necessary once these compo- nents are supplied explicitly? We investigate this question through construct-first flow matching, which combines a fitted Gaussian reference, a learned residual ve- locity, and fixed, structure-dependent output transformations. The Gaussian com- ponent is propagated analytically, and the teacher is distilled into one or two neural maps before the output transformations are applied. For the Gaussian reference flow with an isotropic source, we show that uniform-grid Euler requires Θ(√κ) steps to resolve the smallest-variance direction to fixed relative accuracy, where κis the ratio of source variance to the smallest data variance. Analytic propaga- tion eliminates this component’s discretisation error. On six short-window bench- marks, we evaluate generation using splits without timestamp overlap, memori- sation diagnostics, and re-evaluation on a separate test split. Among configura- tions not flagged by the diagnostics, our method achieves the lowest RFF-C2ST score on four datasets on both evaluation splits, using zero to two neural evalua- tions. Ablations reveal distinct contributions: learned dynamics improve ETTh1 and Stock, interact beneficially with the transformations on Energy, and are not required to attain the reported scores on Sines, MuJoCo, and fMRI. These results show where direct statistical construction can replace neural generation and where combining the two remains beneficial.