Fourier, Wavelet and Signature Losses Fix the Spectral Mismatch in Latent Flow Time Series Generators

arXiv 2609.21989·low signalXBlueskyLinkedInCopy link

Latent flow models generate time series cheaply but the latent compression introduces artifacts, notably a spectral mismatch against the source dataset that makes the synthetic data unsuitable as a training surrogate. The authors fine-tune the latent space with losses built on canonical signal representations, Fourier, wavelet and signature transforms, so the latent preserves the dynamical properties that matter rather than optimizing pointwise reconstruction. Against a base latent-flow model and the state of the art on real-world long-range univariate and multivariate benchmarks, the aligned models win on signal-realness metrics and computational efficiency while staying aligned to the training set's local structure.