HyFAD: Hybrid Time-Frequency Diffusion with Frequency-Aware Embedding for Time Series Imputation

2026-06-03

AI Summary

Existing diffusion models struggle to simultaneously capture global trends and local dynamics in time series imputation and often fail to effectively reconstruct high-frequency components. To address this, this work proposes a time–frequency coupled diffusion mechanism within the DDPM framework: it first models low-frequency global structures in the time domain and then refines high-frequency details in the frequency domain. A key innovation is the introduction of frequency-aware step embeddings, which dynamically associate diffusion timesteps with spectral components, enabling band-specific denoising and reconstruction. This approach achieves state-of-the-art performance across multiple benchmark datasets and represents the first method to enable synergistic optimization of time- and frequency-domain information throughout the diffusion process.

Abstract

Diffusion models have demonstrated strong performance in time series modeling due to their ability to progressively capture complex data distributions through iterative denoising. However, existing approaches struggle with frequency-sensitive denoising, high-frequency reconstruction and balancing global trends with local dynamics. To address these limitations, we propose \textbf{HyFAD}, a \textbf{Hy}brid time-frequency \textbf{D}iffusion model with \textbf{F}requency-\textbf{A}ware embedding for time series imputation. Built upon the DDPM paradigm, HyFAD adopts a coupled time-frequency diffusion framework, in which the reverse denoising proceeds sequentially from the time domain to the frequency domain, enabling coarse-to-fine generation. Specifically, the time-domain diffusion process captures low-frequency global trends, while the frequency-domain diffusion process refines high-frequency spectral components. We further introduce a frequency-aware step embedding that exploits the relationship between diffusion steps and spectral components, providing step-dependent spectral guidance and facilitates more accurate band-wise reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that HyFAD achieves state-of-the-art performance. Our source code is available at https://github.com/hongfangao/HyFAD.

Problem

• time series imputation
• diffusion models
• frequency-sensitive denoising
• high-frequency reconstruction
• global-local dynamics

Innovation

• hybrid time-frequency diffusion
• frequency-aware embedding
• time series imputation
• spectral reconstruction
• diffusion models