Wavelet Flow Matching for Time Series

Synthetic time series are increasingly needed for data augmentation, privacy-preserving data sharing, and the evaluation of downstream learning systems, yet faithfully reproducing the multi-scale temporal structure and the cross-channel dependencies of real-world signals remains challenging. In this work we study generative modeling of multivariate time series by flow matching in the wavelet domain. Rather than learning the flow in the time domain, we learn it on the multilevel discrete wavelet coefficients of each window, a representation that places coarse trend and successively finer detail in separate levels and thus exposes the multi-scale structure directly to the model. The transform is applied to each channel independently, so it reorganizes temporal structure while leaving the dependence between channels entirely to the network. We therefore parametrize the velocity field with a transformer in which each token is a single channel, carrying its coefficients across all decomposition levels, so that attention acts directly across channels. We further derive a family of learnable orthonormal wavelets from the lattice factorization of paraunitary filter banks, with perfect reconstruction guaranteed at every training step, and find performance largely insensitive to the choice of filter, fixed or learned. We compare the resulting model against five recent generative models on seven benchmark datasets at four sequence lengths, using discriminative, predictive, correlational, and Context-FID scores. Our model is best or tied on a majority of the dataset–metric combinations at every window length, with the largest and most consistent gains on Context-FID and the discriminative score.