We propose a deep generative framework for multi-view learning based on a probabilistic interpretation of canonical correlation analysis (CCA). The model combines a linear multi-view layer in the latent space with deep generative networks as observation models, to decompose the variability in multiple views into a shared latent representation that describes the common underlying sources of variation and a set of viewspecific components. To approximate the posterior distribution of the latent multi-view layer, an efficient variational inference procedure is developed based on the solution of probabilistic CCA. The model is then generalized to an arbitrary number of views. An empirical analysis confirms that the proposed deep multi-view model can discover subtle relationships between multiple views and recover rich representations.