Flow Matching with Semidiscrete Couplings
arXiv:2509.25519v2 Announce Type: replace-cross Abstract: Flow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points $(mathbf{x}_0,mathbf{x}_1)$ and ensuring that the velocity field is aligned, on average, with $mathbf{x}_1-mathbf{x}_0$ when evaluated along a segment linking $mathbf{x}_0$ to $mathbf{x}_1$. While these pairs are sampled independently by default, they can also be selected more carefully by matching […]