This project will focus on the further development and analysis of generative models. Examples of such models include Generative Adversarial Networks (GANs), energy-based models, normalising flows, diffusion models, and score-based generative models. Wasserstein gradient flows of various metrics applied to the training of such models will be investigated. For example, Wasserstein gradient flows of the Kullback-Leibler (KL) divergence or Maximum Mean Discrepancy (MMD), or other metrics. A focus will be placed on evaluating the convergence of these flows to the global optimum, and the associated conditions on the distributions.