Flow matching has emerged as a powerful framework for generative modeling. It is finding increasing application in scientific domains, from molecular design to climate modeling. By directly regressing the velocity field of a deterministic ODE, flow matching simplifies both training and sampling relative to diffusion-based approaches. This tutorial provides a pedagogical introduction to flow matching through the lens of probabilistic inference. We will in particular discuss variational flow matching (VFM), which reframes flow matching as self-supervised prediction of the end point of a trajectory. This perspective enables extensions to discrete and structured domains — essential for molecular and chemical systems — as well as controlled generation via test-time guidance. The tutorial will cover foundational concepts and implementation considerations, and will discuss how these methods can be applied to scientific challenges involving both discrete objects (molecules, proteins) and continuous fields (spatiotemporal signals in climate and biology).
