Generative Models from the Inside: a journey through properties and applications

Generative Artificial Intelligence (Gen-AI) is a rapidly evolving field focused on developing models that can generate realistic and novel content, from text to images. Recent advancements such as ChatGPT and DALL-E have revolutionized domains like Natural Language Processing and Computer Vision by creating models capable of producing highly realistic and coherent outputs. This increase in generative capabilities has been driven by foundational models like Transformers, Generative Adversarial Networks (GANs), and Diffusion Models, which have expanded the boundaries of what machines can create. This thesis addresses open challenges in the field, including optimizing computational efficiency, analyzing the latent spaces of generative models, and extracting valuable insights from pre-trained models. The contributions of this work include the development of novel recursive architectures, the application of topological data analysis to better understand GAN training dynamics, and the use of diffusion models for training-free segmentation, highlighting the increasing versatility of generative models across diverse applications. The future of Gen-AI is promising, with numerous opportunities yet to be explored. While progress has been significant, much remains to be learned, and further exploration will be essential to fully realize the potential of these models. We hope that this thesis will provide a meaningful contribution to inspire a deeper understanding and development of generative modelling.