  We present a method for learning latent stochastic differential equations
(SDEs) from high-dimensional time series data. Given a high-dimensional time
series generated from a lower dimensional latent unknown It\^o process, the
proposed method learns the mapping from ambient to latent space, and the
underlying SDE coefficients, through a self-supervised learning approach. Using
the framework of variational autoencoders, we consider a conditional generative
model for the data based on the Euler-Maruyama approximation of SDE solutions.
Furthermore, we use recent results on identifiability of latent variable models
to show that the proposed model can recover not only the underlying SDE
coefficients, but also the original latent variables, up to an isometry, in the
limit of infinite data. We validate the method through several simulated video
processing tasks, where the underlying SDE is known, and through real world
datasets.
