Many phenomena in physics, chemistry, astronomy, and biology can be modelled by differential equations, but their exact form is often unknown. A main ongoing scientific challenge is discovering such equations based on a combination of physical insight and data-driven techniques. Neural differential equations provide a promising hybrid framework in which physics and neural networks can be combined, however they struggle to model chaotic problems such as turbulence. We propose to add stochastic terms and employ neural stochastic differential equations to perform probabilistic turbulence simulations. We develop a new method for discovering such equations by exploiting recent generative machine learning approaches.