  Structuring the latent space in probabilistic deep generative models, e.g.,
variational autoencoders (VAEs), is important to yield more expressive models
and interpretable representations, and to avoid overfitting. One way to achieve
this objective is to impose a sparsity constraint on the latent variables,
e.g., via a Laplace prior. However, such approaches usually complicate the
training phase, and they sacrifice the reconstruction quality to promote
sparsity. In this paper, we propose a simple yet effective methodology to
structure the latent space via a sparsity-promoting dictionary model, which
assumes that each latent code can be written as a sparse linear combination of
a dictionary's columns. In particular, we leverage a computationally efficient
and tuning-free method, which relies on a zero-mean Gaussian latent prior with
learnable variances. We derive a variational inference scheme to train the
model. Experiments on speech generative modeling demonstrate the advantage of
the proposed approach over competing techniques, since it promotes sparsity
while not deteriorating the output speech quality.
