Active inference (AIF), grounded in the free energy principle, provides a unified framework for learning and decision-making under uncertainty. However, standard computational AIF formulations are restricted to finite state spaces and discrete time, limiting their applicability in environments with continuous space and time. To address this, we parameterise continuous-time state evolutions with neural stochastic differential equations (NSDEs), whose neural-network–based drift and diffusion can flexibly capture complex, nonlinear stochastic dynamics in high-dimensional state spaces. By embedding these NSDEs in a variational inference architecture, we derive a continuous-time expected free energy objective and show how to optimise it using established stochastic differential equation (SDE) solvers and Monte Carlo sampling. In particular, we show that continuous-time AIF naturally accommodates irregular or sporadic time series data, accurately recovering observed dynamics and preferred outcomes on a synthetic benchmark while outperforming fixed-step baselines. These results demonstrate that our NSDE-based AIF preserves the stochastic nature of AIF in continuous time while remaining grounded in mathematical theory and computational methods for SDEs.