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

Neural Stochastic Differential Equations(SDEs) are widely adopted for modeling irregular time series which is ubiquitous in the real world. We introduce SDE-VI, a novel variational inference framework for generative modeling of irregular time series that proposes a paradigm shift from learning posterior SDE over the whole continuous time interval directly to the SDE-induced joint distribution over discrete-time observations. Specifically, we directly learn a variational posterior and ensure it is induced by Linear Time-Varying SDEs, as a stable and scalable inference backbone. SDE-VI learns a variational posterior that is guaranteed to be induced by a Linear Time-Varying (LTV) SDE, providing a stable and scalable inference backbone. To overcome the long-standing trade-off between computational efficiency and expressivity in prior work, we further generalize the framework to nonlinear, complex-valued SDEinduced variational inference, enabling intricate dynamics modeling for real-world data. Extensive experiments across healthcare, physics, climate, and IoT benchmarks demonstrate state-of-the-art performance on interpolation, extrapolation, regression, and classification tasks.