Variance-Corrected Wavelet Diffusion for Industrial Sensor Signal Augmentation and Denoising

Multivariate time series play a critical role in industrial production for monitoring, anomaly detection, and failure prediction, yet real-world scenarios often suffer from data scarcity and class imbalance, limiting the effectiveness of deep learning models. Existing generative approaches, such as GANs and VAEs, still face challenges in complex time-series generation, including training instability, mode collapse, and limited ability to capture intricate temporal dynamics, making reliable deployment in industrial applications difficult. These limitations highlight the need for a more stable, controllable, and high-fidelity generative framework. To address the aforementioned challenges, we propose VC-WaveDiff, a diffusion-based generative framework specifically designed for time-series data. It tightly integrates our newly developed WaveTS-UNet with a denoising diffusion model to enable multiscale structural modeling and stable high-quality synthesis. WaveTS-UNet incorporates a wavelet-based decomposition-reconstruction module tailored for time-series characteristics, which uses fixed wavelet filters to explicitly separate trend and rapidly varying components, achieving multiscale representation learning with linear computational complexity. Within the diffusion framework, VC-WaveDiff analytically derives the optimal variance of the reverse process, allowing the model to follow a standard diffusion training procedure and generate high-quality samples adaptively at inference without additional training. Furthermore, a continuous noise scheduling function is introduced to unify discrete and continuous diffusion processes, enabling the generative trajectory to better reflect the inherent continuity of time series. Experiments on two public sensor datasets show that VC-WaveDiff generates diverse and high-fidelity time series under conditions of data scarcity or class imbalance, significantly improving downstream task performance and demonstrating its practical value for industrial AI applications.