Time series generation with spectrally aligned latent flow matching

Latent flow models have proven to be a reliable and cost-effective method for time series generation. However, the latent compression induces unwanted artefacts, such as a spectral mismatch with respect to the underlying dataset, thus hindering their use as training surrogates. In this article, we propose a spectrally-aligned latent-flow time series generator, where the latent space for flow matching is trained to preserve dynamical properties that are relevant for the suitability of synthetic samples. We find that incorporating fine-tuning losses based on canonical signal representations such as the Fourier, wavelet and signature transforms helps overcome these issues. The interpretability of these transformations allows us to ensure that the synthetic signals are aligned with the true ones in terms of relevant features, such as smoothness or targeted spectral content, as opposed to relying on pointwise reconstruction losses only. We compare the proposed aligned models against a base latent-flow model and the state of the art over real-world long-range univariate and multivariate benchmark datasets. Our quantitative results validate the superiority of the proposed method in terms of its performance on metrics reflecting signal realness and computational efficiency, while being aligned to the training set with respect to its local structure.