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In deep latent Gaussian models, the latent variable is generated by atime-inhomogeneous Markov chain, where at each time step we pass the currentstate through a parametric nonlinear map, such as a feedforward neural net, andadd a small independent Gaussian perturbation. This work considers thediffusion limit of such models, where the number of layers tends to infinity,while the step size and the noise variance tend to zero. The limiting latentobject is an It\^o diffusion process that solves a stochastic differentialequation (SDE) whose drift and diffusion coefficient are implemented by neuralnets. We develop a variational inference framework for these \textit{neuralSDEs} via stochastic automatic differentiation in Wiener space, where thevariational approximations to the posterior are obtained by Girsanov(mean-shift) transformation of the standard Wiener process and the computationof gradients is based on the theory of stochastic flows. This permits the useof black-box SDE solvers and automatic differentiation for end-to-endinference. Experimental results with synthetic data are provided.

Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit