Generative modeling aims to capture and sample complex high-dimensional data distributions, playing a central role in machine learning, Bayesian inference and computational physics. This PhD project focuses on Hamiltonian and non-reversible flow-based generative models, a promising alternative to diffusion models and traditional normalizing flows. Normalizing Hamiltonian Flows (NHFs) offer stability, interpretability, and reduced computational cost by leveraging symplectic, volume-preserving dynamics. The goal is to develop more flexible and scalable NHF architectures and explore non-reversible stochastic flows to build state-of-the-art generative tools. The student will join Université Clermont-Auvergne’s Laboratoire de Mathématiques Blaise Pascal within the interdisciplinary Cluster IA chair R-GAINS, at the interface of stochastic processes, statistical physics, and machine learning. The project involves collaborations with LMBP, ICCF, and LIPhy (U. Grenoble-Alpes). We seek motivated candidates with a background in probability, statistical physics, or computational physics and an interest in generative modeling. Programming skills are strongly appreciated.