Generative Self-Supervised Time-Series Forecasting Leveraging Wavelet Diffusion

Measurement data often exhibit multi-scale periodicity and nonlinear noise, posing significant challenges for accurate long-term forecasting in modern instrumentation and control systems. Despite the considerable advances that Transformer-based self-attention mechanisms have brought to long-term time series forecasting (LTSF),various existing approaches overlook the multi-frequency structure and intricate noise patterns inherent in real-world measurement signals. To address these challenges, we propose TimeWaveDiff, a generative self-supervised framework that integrates wavelet decomposition and a diffusion model for time series instrumentation signal forecasting. Specifically, wavelet transforms are applied to patched multivariate measurement data, achieving fine-grained multi-scale frequency decomposition that preserves both global trends and local fluctuations. A diffusion process then progressively adds and removes noise, enabling robust learning of nonlinear dynamics and complex noise distributions often encountered in sensor-driven measurements. Furthermore, TimeWaveDiff replaces a heavy encoder–decoder design with a lightweight feedforward network enhanced by seasonal–trend decomposition, significantly reducing computational costs while maintaining predictive accuracy. Extensive experiments on public datasets show that TimeWaveDiff achieves superior MSE and MAE performance for long-term forecasting. Ablation studies, efficiency analyses, and visualization results reinforce the complementary synergy between wavelet decomposition and diffusion while illustrating the interpretability of the proposed approach. Overall, Time-WaveDiff provides a robust, efficient solution for forecasting complex, dynamic time series and offers valuable insights for future research in self-supervised learning.