Abstract:
Flow matching provides a scalable framework for training continuous normalizing flows and has consequently gained popularity in generative modelling. Its close connection to continuous-time dynamics has also made it increasingly relevant to scientific applications, including cellular trajectory inference, weather forecasting, and the modelling of physical systems.
However, standard flow-matching methods often rely on design choices that do not reflect the underlying structure or prior knowledge of the scientific process being modelled. As a result, a model may generate samples that are statistically plausible while remaining scientifically or mechanistically implausible.
In this talk, I will discuss how flow-matching models can be grounded in prior domain knowledge through a more principled design of their conditional probability paths. I will focus on two complementary approaches developed in our work: ContextFlow, which incorporates biological knowledge into optimal-transport couplings for modelling cellular dynamics, and SplineFlow, which uses B-spline conditional paths to better reflect the smooth, nonlinear evolution of dynamical systems. Together, these methods illustrate how prior knowledge can be introduced at different stages of the flow-matching framework to improve the scientific plausibility of learned dynamics.
