Generative models have recently emerged as powerful frameworks for data synthesis, representation learning, and the modelling of complex high-dimensional distributions. However, their deployment in scientific and engineering domains remains challenging, as data are often scarce, noisy, heterogeneous, or inherently distributed across multiple clients or institutions. In this project, we will develop reliable, efficient, and scalable flow matching methods for learning from limited and distributed data. A central focus will be federated flow matching, where raw data cannot be shared due to privacy, ownership, or regulatory constraints. We will design and evaluate algorithms that enable the collaborative training of high-quality generative models while addressing key challenges in federated learning, including communication efficiency, privacy protection, robustness to heterogeneous client data, and fairness across groups. A second focus will be on improving the controllability of flow matching models through constrained and risk-sensitive optimization. By introducing constraints and risk-sensitive objectives in probability measure space, we will formulate novel fine-tuning problems and develop efficient algorithms for solving them. These formulations will be applied to scientific discovery and robotic trajectory generation tasks.