Title: Frequency Decomposition and Enhancement for Time Series Generation Using Diffusion Models
Primary area: learning on time series and dynamical systems
Keywords: Diffusion, Time Series, Frequency Decomposition, Generation

Abstract: Time series data are essential in domains such as finance, healthcare, energy management, climate prediction, and AIOps, yet the scarcity of large-scale, high-quality training datasets often restricts the performance of machine learning solutions. Synthetic data generation, particularly through diffusion models, has become a promising strategy to address these limitations. Diffusion-based models have showcased impressive results, but face challenges in capturing diverse frequency components and retaining high-frequency details during noise accumulation. To address these issues, we propose a multi-stage diffusion framework named Frequency Decomposed and Enhanced Diffusion (\gen), which explicitly decomposes time series into low- and high-frequency signals and emphasizes preserving fine-grained temporal patterns. Our method first trains an unconditional generator on coarse, periodic low-frequency signals, then incorporates an enhancement mechanism to synthesize precise high-frequency details. This two-stage approach systematically handles complex temporal variations, allowing \gen to produce more accurate, realistic, and diverse time series. We conduct extensive experiments on publicly available real-world datasets, demonstrating that \gen not only outperforms state-of-the-art generative methods in various evolution metrics but also exhibits superior adaptability across different time series domains. An ablation study confirms the effectiveness of frequency decomposition and high-frequency enhancement, underscoring the advantage of exploiting multi-resolution insights. Our findings expand the application scope of diffusion models for time series generation tasks, offering a flexible solution for data augmentation under privacy and sensitivity constraints. We have made our code anonymously available at \codeurl{}.