Physiologically-aware data generation: A differentiable HMM and frequency-domain Transformer GAN approach

The generation of multivariate medical time series, such as intensive care unit (ICU) trajectories, remains challenging because patient signals are highly heterogeneous, non-stationary, and strongly multimodal. In this paper, we present a methodological proof-of-concept for the structural fusion of probabilistic graphical models and deep generative adversarial networks. Rather than relying on an unconstrained Gaussian latent prior, the proposed method uses a Tempered Metropolis–Hastings sampler to refine latent codes and a differentiable hidden Markov model (dHMM) to provide clinically informed conditioning. The generator then synthesizes physiological sequences from this refined latent representation, while the discriminator encourages realism and stability during training. Experiments on the MIMIC-III database show that HMM-GAN achieves stronger fidelity than TimEHR and TimeGAN across most metrics, with Precision of 0.860, Recall of 0.693, Density of 0.621, and Coverage of 0.741. In downstream utility evaluation, the proposed model also improves mortality prediction, attaining an AUROC of 0.662 and an AUPRC of 0.710, compared with 0.5183/0.5338 for TimEHR and 0.479/0.479 for TimeGAN. Privacy analysis further indicates that HMM-GAN maintains a favorable trade-off between utility and confidentiality, with JSD MIA = 0.085 and NNAA risk of 0.0253. These results suggest that combining dHMM conditioning with tempered sampling provides a promising direction for generating realistic and diverse synthetic biomedical time series.