FSDI: Frequency-Shaped Diffusion For Time-Series Imputation

In real-world web applications, especially those involving sensor networks and Internet of Things (IoT) devices, time series data are often incomplete due to network delays, device failures or logging constraints. Such missing data can severely affect downstream tasks including anomaly detection, recommendation, and A/B testing, making imputation a critical step for reliable web analytics. Diffusion models have recently achieved strong performance for time series imputation. As relevant research progresses, the spectral nature of time series has received increasing attention. However, most ''frequency-aware'' diffusion variants modify either the input or network architecture, but the variance schedule in the forward process remains unchanged, injecting noise with the same variance into every frequency bin. This limitation prevents diffusion from adapting to real data, where spectral energy varies irregularly across frequencies rather than following a simple high–low split. To address these issues, we propose Frequency-Shaped Diffusion (FSDI), which replaces the uniform variance schedule with a data-driven schedule in the frequency domain. Frequency bin variances are estimated from the spectral energy distribution of the data, allocated as inverses of that energy, and then Parseval-calibrated so the total noise energy exactly matches standard diffusion, preserving training stability and ensuring fair comparison. Experiments on real-world datasets demonstrate that FSDI achieves state-of-the-art performance. All code have been made publicly at https://github.com/decisionintelligence/FSDI.