Effective Series Decomposition and Components Learning for Time Series Generation

TL;DR

The paper tackles the challenge of realistically generating multivariate time series with interpretable components. It introduces STDiffusion, a diffusion-based framework that applies a Learnable Moving Average to extract explicit trend and seasonality from raw data, complemented by a learnable wavelet-based seasonal decomposition and frequency attention. A Seasonal-Trend Correction module enforces high-order dependencies and coherent joint dynamics between components, improving temporal consistency. Across eight real-world datasets, STDiffusion achieves state-of-the-art generation performance and demonstrates robustness for long-sequence generation, while offering interpretable, component-wise representations of time-series structure.

Abstract

Time series generation focuses on modeling the underlying data distribution and resampling to produce authentic time series data. Key components, such as trend and seasonality, drive temporal fluctuations, yet many existing approaches fail to employ interpretative decomposition methods, limiting their ability to synthesize meaningful trend and seasonal patterns. To address this gap, we introduce Seasonal-Trend Diffusion (STDiffusion), a novel framework for multivariate time series generation that integrates diffusion probabilistic models with advanced learnable series decomposition techniques, enhancing the interpretability of the generation process. Our approach separates the trend and seasonal learning into distinct blocks: a Multi-Layer Perceptron (MLP) structure captures the trend, while adaptive wavelet distillation facilitates effective multi-resolution learning of seasonal components. This decomposition improves the interpretability of the model on multiple scales. In addition, we designed a comprehensive correction mechanism aimed at ensuring that the generated components exhibit a high degree of internal consistency and preserve meaningful interrelationships with one another. Our empirical studies on eight real-world datasets demonstrate that STDiffusion achieves state-of-the-art performance in time series generation tasks. Furthermore, we extend the model's application to multi-window long-sequence time series generation, which delivered reliable results and highlighted its robustness and versatility.

Figures (8)

• Figure 1: Illustrations of model structure consists of two parts: (a)A diffusion model schema involving add-noise and de-noise stages. (b) STDiffusion model essential components and pipeline.
• Figure 2: Learnable Moving Average pipeline: (a) upper part depicts the decomposition, and (b) lower part describes the restoration. $\oplus$ refers element-wise addition, and $\ominus$ refers element-wise deduction.
• Figure 3: Seasonal-Trend Correction module. Predicted trend and seasonality are refined via cross-attention between input and conditional branches.
• Figure 4: t-SNE visualizations (top row) compare the original data (red dots) with samples generated by STDiffusion (blue dots). The bottom row presents data density estimates, showing how the distributions of STDiffusion (blue lines) and Diffusion-TS (green lines) align with the ground truth (red lines).
• Figure 5: Results on ETTh1, ETTh2, and Exchange datasets. Bars show the average scores with 95% confidence intervals for sequence lengths 64, 128, and 256. Lower values indicate better performance across all metrics. Additional score details is provided on the Github Repo https://github.com/mobkageyama/STDiffusion.