The Variational Autoencoder (VAE) is a powerful deep generative model that is now extensively used to represent high-dimensional complex data via a low-dimensional latent space learned in an unsupervised manner. In the original VAE model, input data vectors are processed independently. In recent years, a series of papers have presented different extensions of the VAE to process sequential data, that not only model the latent space, but also model 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 an extensive literature review of these models. Importantly, we introduce and discuss a general class of models called Dynamical Variational Autoencoders (DVAEs) that encompasses a large subset of these temporal VAE extensions. Then we present in detail seven different instances of DVAE that were recently proposed in the literature, with an effort to homogenize the notations and presentation lines, as well as to relate these models with existing classical temporal models. We reimplemented those seven DVAE models and we present the results of an experimental benchmark conducted on the speech analysis-resynthesis task (the PyTorch code is made publicly available). The paper is concluded with an extensive discussion on important issues concerning the DVAE class of models and future research guidelines.
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