Generative modeling has seen a huge explosion in the last decade, and it is currently a hot topic in Statistics and Machine Learning. The current state-of-the-art is dominated by diffusion-based generative models; however, these are expensive to train and incur a high cost in generating new data. This project aims to explore generative models based on Generative Adversarial Networks (GANs) and Normalizing Flows (NFs). These models fell out of fashion when diffusion models were developed for generative modeling, but recent works are reviving interest in them and point to the opportunities offered by their formulation. This project aims at investigating recent trends in GANs and NFs on Bayesian model selection and multimodality. Some relevant references: - https://arxiv.org/abs/2507.00651 - https://arxiv.org/abs/2501.05441 - https://arxiv.org/abs/2412.06329

- A short review of the literature on GANs and NFs for generative modeling, with emphasis on model selection (architecture search) and multimodality (e.g., text to image generation)

- An experimental validation of ideas aimed at improving the current state-of-the-art in GANs and NFs using appropriate validation metrics

- The drafting of a scientific report containing the proposed methods, experiments, and their analysis.