Conference Agenda

Flow Matching (introduced by Lipman et. al.) and associated models have recently attracted significant interest due to their simulation-free training via a straightforward least squares criterion and the extremely broad and consequently adaptable underlying ordinary differential equation framework. Despite being a generative model that aims to mimic an unknown distribution, its possible applications extend far beyond the core task of generating new samples. The cheap generation of new samples opens the door to efficient distribution estimation, an essential component of forecasting tasks such as weather prediction. In this talk, we first adapt the Flow Matching method to smooth conditional density estimation. We show that the resulting estimator is closely related to th Nadaraya-Watson estimator. Then, we bridge the gap between proper scoring rules, the established method of evaluating predictions, and the fundamental concept of risk in statistical learning. Building on this, we show that the Nadaraya-Watson estimator achieves a minimax optimal anisotropic rate of convergence with respect to the risk associated with the Fourier score. In the end, we transfer this result to the Flow Matching estimator and demonstrate its capability in practice.