  Density estimation, compression and data generation are crucial tasks in
artificial intelligence. Variational Auto-Encoders (VAEs) constitute a single
framework to achieve these goals. Here, we present a novel class of generative
models, called self-supervised Variational Auto-Encoder (selfVAE), that
utilizes deterministic and discrete variational posteriors. This class of
models allows to perform both conditional and unconditional sampling, while
simplifying the objective function. First, we use a single self-supervised
transformation as a latent variable, where a transformation is either
downscaling or edge detection. Next, we consider a hierarchical architecture,
i.e., multiple transformations, and we show its benefits compared to the VAE.
The flexibility of selfVAE in data reconstruction finds a particularly
interesting use case in data compression tasks, where we can trade-off memory
for better data quality, and vice-versa. We present performance of our approach
on three benchmark image data (Cifar10, Imagenette64, and CelebA).
