Dynamic community detection using class preserving time series generation with Fourier Markov diffusion

Daozheng Qu, Yanfei Ma, Yibo Wang

Abstract: Generating class-consistent time series necessitates the maintenance of both overarching structure and detailed temporal dynamics–an endeavor that current GAN and diffusion models find challenging. We introduce FMD-GAN, a Fourier–Markov diffusion framework that integrates spectral clustering, state-conditioned frequency-domain noise modulation, and a dual-branch temporal–spectral discriminator to generate realistic and class-consistent sequences. In four UCR datasets (ECG200, GunPoint, FordA, ChlorineConc), FMD-GAN attains state-of-the-art or competitive outcomes, with up to a 50% reduction in FID and consistent enhancements in DTW, class consistency accuracy (CCA), and spectral distance (SD) compared to six representative baselines. Ablation studies validate the roles of spectrum masking, Markov-guided diffusion, and adversarial learning, whilst sensitivity analysis illustrates resilience to hyperparameters. Qualitative visualizations demonstrate significant semantic congruence between actual and produced samples. These findings indicate that the integration of spectral priors with probabilistic diffusion facilitates the production of time series that preserve structure and are cognizant of class distinctions, pertinent to biomedical monitoring, sensor analytics, and Tiny AI systems.