Elaborating on the Value of Flow Matching for Density Estimation

Flow matching provides a simulation free method for training continuous normalizing flows. Key ingredients are an implicit definition of the target flow via direct definition of the conditional flows with respect to a single target sample and a loss function that directly regresses the time dependent vector field against the conditional vector fields with respect to single samples.In this post, the origin of the flow matching formulation for continuous normalizing flows, their generalization as well as their value for density estimation is discussed. Especially, light is shed on their ability to scale well to higher dimensions and therefore enable new applications in the growing research field of Simulation-based Inference.