  Stochastic differential equations (SDEs) are a staple of mathematical
modelling of temporal dynamics. However, a fundamental limitation has been that
such models have typically been relatively inflexible, which recent work
introducing Neural SDEs has sought to solve. Here, we show that the current
classical approach to fitting SDEs may be approached as a special case of
(Wasserstein) GANs, and in doing so the neural and classical regimes may be
brought together. The input noise is Brownian motion, the output samples are
time-evolving paths produced by a numerical solver, and by parameterising a
discriminator as a Neural Controlled Differential Equation (CDE), we obtain
Neural SDEs as (in modern machine learning parlance) continuous-time generative
time series models. Unlike previous work on this problem, this is a direct
extension of the classical approach without reference to either prespecified
statistics or density functions. Arbitrary drift and diffusions are admissible,
so as the Wasserstein loss has a unique global minima, in the infinite data
limit any SDE may be learnt. Example code has been made available as part of
the \texttt{torchsde} repository.
