Generative Modeling of Irregular Time Series via SDE-Induced Continuous-Discrete Variational Inference

Irregular time series arise ubiquitously in real-world systems, where observations are sparse, asynchronous, and governed by underlying continuous-time dynamics. Existing continuous–discrete state-space models typically rely on path-based variational inference, which is computationally expensive or constrained by restrictive posterior assumptions. We propose SDEVI, a novel framework that performs variational inference directly on the joint distribution over discrete-time observations, while guaranteeing consistency with an underlying continuous process governed by a Stochastic Differential Equation(SDE). SDEVI employs a variational posterior induced by linear time-varying SDEs as a scalable inference backbone. To enable intricate dynamics modeling for real-world data, we introduce non-linear-SDE-induced variational inference and generalize our framework to the complex domain. Extensive experiments across healthcare, physics, climate, and IoT benchmarks demonstrate state-of-the-art performance on interpolation, extrapolation, regression, and classification tasks.