TFD: Spectrally Guided Time–Frequency Diffusion Model For Time Series Imputation

Hongfan Gao, Wangmeng Shen, Bin Yang, Jilin Hu

Keywords: diffusion, time series imputation

TL;DR: We propose a time-frequency hybrid diffusion model and frequency-aware high-pass diffusion embedding for time series imputation task.

Abstract: Diffusion models have recently shown strong advantages in generative modeling and time-series tasks thanks to its capability of accurately capturing complex data distributions through progressive denoising. However, existing time-domain only diffusion models struggle to reconstruct high-frequency details due to non-uniform energy distribution in real-world time series data. To balance the reconstruction of global trends and local dynamics, we introduce \textbf{TFD}, spectrally guided \textbf{T}ime–\textbf{F}requency \textbf{D}iffusion model for time series imputation. TFD is a hybrid time-frequency diffusion framework that couples time and frequency domain diffusion processes to achieve coarse-to-fine reconstruction, and we formalize both the noise-injection and denoising procedures following the DDPM framework. In the proposed hybrid framework, the time-domain diffusion stabilizes low-frequency trends by capturing temporal dependencies, while the frequency-domain counterpart leverages band-separable spectral representations to refine high-frequency details. We further analyze the correspondence between denoising steps and spectral components. Based on this observation, we design a frequency-aware high-pass timestep embedding that serves as spectral guidance, emphasizing the relevant bands at specific steps and enabling more accurate band-wise reconstruction. Extensive experiments demonstrate that our proposed TFD achieves state-of-the-art results across multiple benchmark datasets.

Primary Area: learning on time series and dynamical systems

Submission Number: 8761