Hybrid Diffusion Model for Sequential Data Generation

Sequential data are ubiquitous in real-world applications, and generating realistic sequences is useful for simulation, data augmentation, and forecasting. Diffusion models have become a leading approach for this task, but standard time-domain diffusion treats the sequence as a whole and tends to capture global patterns more faithfully than local variations. Prior frequency-aware methods have added frequency information to time-domain models or moved diffusion entirely to the frequency domain; both approaches still use a single-domain generation process. We propose a Hybrid Diffusion Model that couples low-frequency generation in the time domain with high-frequency generation in the frequency domain. We decompose each sequence into low- and high-frequency components using the discrete Fourier transform and generate them with two diffusion processes that use different domains and schedules. The frequency-domain process runs on the full spectrum with a longer diffusion schedule. During joint sampling, the low-frequency component is generated by the shorter time-domain process, conditioned on the evolving high-frequency state from the frequency-domain process. On five real-world datasets, Hybrid Diffusion outperforms both single-domain diffusion baselines on performance metrics in both the time and frequency domains; on four additional datasets, it achieves the best mean performance in 10 of 12 dataset–metric comparisons against six time-series generative models.