FMD-GAN: Generating Realistic and Class-Preserving Time Series with Neural Networks via Fourier–Markov Diffusion

Yanfei Ma, Daozheng Qu

Abstract: Generating class-consistent time series is a complex endeavor, necessitating both structural integrity and semantic coherence. This study presents FMD-GAN, a generative framework that integrates frequency-domain segmentation with Markov-conditioned diffusion to produce realistic and interpretable sequences. Through the integration of spectral clustering, state-conditioned noise injection, and dual-branch adversarial learning, FMD-GAN maintains class semantics while effectively capturing dynamic temporal patterns. Experiments on four UCR datasets indicate that FMD-GAN attains performance that is either competitive or superior to six leading generative baselines across FID, DTW, class consistency accuracy (CCA), and spectral distance (SD). Supplementary analyses—such as t-SNE visualizations, ablation studies, and training dynamics—underscore the model’s stability, interpretability, and resilience to hyperparameter fluctuations. These findings highlight the efficacy of integrating spectral priors with probabilistic frameworks in enhancing class-aware time series production.