Flow matching avoids the curse of dimensionality by adapting to intrinsic data dimension
Chakraborty et al. derive finite-sample generalization bounds for flow-matching generative models. They show that the Wasserstein-p distance between the learned and true distribution scales as n^{-1/d} where d is the intrinsic dimension of the data, not the much larger ambient dimension. This result explains why flow matching succeeds on high-dimensional data that lie on low-dimensional manifolds.
