WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generation

TMLR Paper9047 Authors

Abstract: Time series are ubiquitous in many applications that involve forecasting, classification and causal inference tasks, such as healthcare, finance, audio signal processing and climate sciences. Still, large, high-quality time series datasets remain scarce. Synthetic generation can address this limitation; however, current models confined either to the time or frequency domains struggle to reproduce the inherently multi-scaled structure of real-world time series. We introduce WaveletDiff, a new framework that trains diffusion models directly on wavelet coefficients to exploit the inherent multi-resolution structure of time series data. The model combines dedicated transformers for each decomposition level with cross-level attention mechanisms that enable selective information exchange between temporal and frequency scales through adaptive gating. It is also informed by level-specific energy constraints based on Parseval's theorem which preserve time-frequency properties throughout the diffusion process. Comprehensive tests across six real-world datasets from energy, finance, and neuroscience domains demonstrate that WaveletDiff consistently outperforms state-of-the-art time-domain and frequency-domain generative methods on both short and long time series across five diverse performance metrics. For example, WaveletDiff achieves discriminative scores and Context-FID scores that are $3\times$ smaller on average than the second-best baseline across all datasets. Our code is available at https://anonymous.4open.science/r/WaveletDiff-27E9/.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Peilin_Zhao2

Submission Number: 9047