Arthur Stéphanovitch (ENSAE) : Convergence rates for flow-based generative models

We show that, in recent SDE-based generative methods, the drift naturally inherits the regularity of the data distribution. This regularity yields both stability of the underlying SDE and favorable approximation properties of the drift. Leveraging these regularity estimates, we establish optimal statistical and discretization convergence rates for both flow matching and diffusion models.