  Simulation-based techniques such as variants of stochastic Runge-Kutta are
the de facto approach for inference with stochastic differential equations
(SDEs) in machine learning. These methods are general-purpose and used with
parametric and non-parametric models, and neural SDEs. Stochastic Runge-Kutta
relies on the use of sampling schemes that can be inefficient in high
dimensions. We address this issue by revisiting the classical SDE literature
and derive direct approximations to the (typically intractable)
Fokker-Planck-Kolmogorov equation by matching moments. We show how this
workflow is fast, scales to high-dimensional latent spaces, and is applicable
to scarce-data applications, where a non-parametric SDE with a driving Gaussian
process velocity field specifies the model.
