We derive reverse-mode (or adjoint) automatic differentiation for solutions of stochastic differential equations (SDEs), allowing time-efficient and constant-memory computation of pathwise gradients, a continuous-time analogue of the reparameterization trick.
 Specifically, we construct a backward SDE whose solution is the gradient and provide conditions under which numerical solutions converge.
 We also combine our stochastic adjoint approach with a stochastic variational inference scheme for continuous-time SDE models, allowing us to learn distributions over functions using stochastic gradient descent.
 Our latent SDE model achieves competitive performance compared to existing approaches on time series modeling.

We present a constant memory gradient computation procedure through solutions of stochastic differential equations (SDEs) and apply the method for learning latent SDE models.