  The adjoint sensitivity method scalably computes gradients of solutions to
ordinary differential equations. We generalize this method to stochastic
differential equations, allowing time-efficient and constant-memory computation
of gradients with high-order adaptive solvers. Specifically, we derive a
stochastic differential equation whose solution is the gradient, a
memory-efficient algorithm for caching noise, and conditions under which
numerical solutions converge. In addition, we combine our method with
gradient-based stochastic variational inference for latent stochastic
differential equations. We use our method to fit stochastic dynamics defined by
neural networks, achieving competitive performance on a 50-dimensional motion
capture dataset.
