WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generation

2025-10-13

AI Summary

Real-world time series exhibit complex multi-scale structures; existing generative models—limited to single-domain (time- or frequency-domain) modeling—struggle to faithfully reconstruct such structures, hindering high-fidelity synthetic dataset construction. To address this, we propose a wavelet-coefficient-based hierarchical diffusion framework. Our method introduces a novel cross-level attention mechanism and a Parseval-theorem-driven energy conservation constraint, enabling adaptive inter-scale information exchange and spectral fidelity preservation between time and frequency domains. Integrating wavelet transforms, diffusion modeling, and Transformer architectures, the framework achieves state-of-the-art performance across six real-world time-series benchmarks: discriminative scores and Context-FID improve by an average factor of three, while both generation quality and diversity increase simultaneously. This work establishes a new paradigm for time-series synthesis and analysis in healthcare, finance, climate science, and related domains.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Time-Series/Data Streams
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

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 novel 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 also incorporates energy preservation constraints for individual levels based on Parseval's theorem to preserve spectral fidelity 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 $3 imes$ smaller on average than the second-best baseline across all datasets.

Problem

• Generating high-quality synthetic time series data
• Capturing multi-scaled structure across time-frequency domains
• Overcoming limitations of single-domain generative models

Innovation

• Trains diffusion models on wavelet coefficients
• Combines transformers with cross-level attention mechanisms
• Incorporates energy preservation constraints via Parseval's theorem