  We present a Bayesian non-parametric way of inferring stochastic differential
equations for both regression tasks and continuous-time dynamical modelling.
The work has high emphasis on the stochastic part of the differential equation,
also known as the diffusion, and modelling it by means of Wishart processes.
Further, we present a semi-parametric approach that allows the framework to
scale to high dimensions. This successfully lead us onto how to model both
latent and auto-regressive temporal systems with conditional heteroskedastic
noise. We provide experimental evidence that modelling diffusion often improves
performance and that this randomness in the differential equation can be
essential to avoid overfitting.
