WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generation

WaveletDiff is a multi-scale wavelet-based diffusion model framework designed to improve the quality of time series generation. The model achieves information exchange between time-frequency scales through adaptive gating, by directly training on wavelet coefficients and combining specialized Transformers at each decomposition level with cross-level attention mechanisms. Specific energy constraints are applied based on Passeval’s theorem to preserve time-frequency characteristics. In tests on six real datasets covering energy, finance, and neuroscience, WaveletDiff outperforms baseline diffusion models such as FourierDiffusion, Diffusion-TS, and SigDiffusions in generation performance. Experiments show that WaveletDiff performs better on most metrics, with discrimination and context FID scores being about one-third of the baseline; compared to MSDformer, it has fewer parameters and shorter training time, but it is slightly inferior to MSDformer on fMRI data, while performing better on EEG data.