Generative modeling of clinical time series via latent stochastic differential equations

Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant challenges due to irregular sampling, complex latent physiology, and inherent uncertainties in both measurements and disease progression. To address these challenges, we propose a generative modeling framework based on latent neural stochastic differential equations (SDEs) that views clinical time series as discrete-time partial observations of an underlying controlled stochastic dynamical system. Our approach models latent dynamics via neural SDEs with modality-dependent emission models, while performing state estimation and parameter learning through variational inference. This formulation naturally handles irregularly sampled observations, learns complex nonlinear interactions, and captures the stochasticity of disease progression and measurement noise within a unified scalable probabilistic framework. We validate the framework on three complementary tasks: (i) individual treatment effect estimation using a simulated pharmacokinetic-pharmacodynamic (PKPD) model of lung cancer, (ii) probabilistic glucose forecasting using synthetic data from the Bergman Minimal Model, and (iii) probabilistic forecasting of physiological signals using real-world intensive care unit (ICU) data from 12,000 patients. Results show that our framework achieves the strongest overall performance compared to latent ordinary differential equation (ODE), controlled differential equation (CDE), and long short-term memory (LSTM) baselines, with consistent advantages in uncertainty calibration across all datasets. These results highlight its potential for enabling precise, uncertainty-aware predictions to support clinical decision-making.