Flow matching, rectified flow matching, minibatch flow matching and optimal transport

par Antonin Chambolle (CEREMADE)

mercredi 13 mai 2026, 10:30 → 12:00 Europe/Paris

Flow matching is an alternative to diffusion methods for sampling from
unknown distributions (of given datasets). While almost equivalent in
the standard case, it has the advantage that it can be applied to any
initial coupling between two distributions, and in particular in a
repeated way, which is the idea of "rectified" flow matching. This
approach is claimed to be a way to compute optimal transport, which is
true only under strong (unverifiable) conditions. We analyse this
process and give examples which show that it should not, in general,
converge to optimal transport. On the other hand, the "minibatch" based
optimisation of rectified flow matching might be a way to approximate
optimal transport, but this also relies on unverifiable conditions,
although less strong than the previous. This is joint work with Julie
Delon and Johannes Hertrich.