  Variational autoencoders (VAEs) are powerful deep generative models widely
used to represent high-dimensional complex data through a low-dimensional
latent space learned in an unsupervised manner. In the original VAE model, the
input data vectors are processed independently. Recently, a series of papers
have presented different extensions of the VAE to process sequential data,
which model not only the latent space but also the temporal dependencies within
a sequence of data vectors and corresponding latent vectors, relying on
recurrent neural networks or state-space models. In this paper, we perform a
literature review of these models. We introduce and discuss a general class of
models, called dynamical variational autoencoders (DVAEs), which encompasses a
large subset of these temporal VAE extensions. Then, we present in detail seven
recently proposed DVAE models, with an aim to homogenize the notations and
presentation lines, as well as to relate these models with existing classical
temporal models. We have reimplemented those seven DVAE models and present the
results of an experimental benchmark conducted on the speech
analysis-resynthesis task (the PyTorch code is made publicly available). The
paper concludes with a discussion on important issues concerning the DVAE class
of models and future research guidelines.
