Comparison of Latent-Space Generative Models through Statistics and Mapping

Although data generation is a task with broad and exciting applications, samples created by generative models often fall victim to reduced variability and biases which, when coupled with the lack of explainability common to all neural networks, makes the evaluation of issues and limitations of these systems challenging. Much effort has been devoted to the exploration of the latent spaces of generative models in order to find more controllable editing directions and to the idea that better models would produce more disentangled representations. In this thesis we present a detailed and comparative analysis of latent-space generative models, beginning from their theoretical foundation and up to a number of statistical and empirical findings. We show that the original data is the sole factor truly impacting how different generative models learn, more than one may imagine: under the same dataset, even very different architectures distribute their latent spaces in essentially the same way. These results suggest new directions of research for representation learning, with the potential to transfer acquired knowledge between models and to understand the common mechanisms behind learning as a whole. Parts of the topics discussed in this thesis are a joint work, particularly those related to the mappings between models; they have already seen publication as a paper.