  We present a representation learning algorithm that learns a low-dimensional
latent dynamical system from high-dimensional \textit{sequential} raw data,
e.g., video. The framework builds upon recent advances in amortized inference
methods that use both an inference network and a refinement procedure to output
samples from a variational distribution given an observation sequence, and
takes advantage of the duality between control and inference to approximately
solve the intractable inference problem using the path integral control
approach. The learned dynamical model can be used to predict and plan the
future states; we also present the efficient planning method that exploits the
learned low-dimensional latent dynamics. Numerical experiments show that the
proposed path-integral control based variational inference method leads to
tighter lower bounds in statistical model learning of sequential data. The
supplementary video: https://youtu.be/xCp35crUoLQ
