Limit Points of Reflow with Minibatch Optimal Transport
Rectified flows, also called flow matching or stochastic interpolants, are generative models that learn a time-dependent vector field steering a probability curve between two probability distributions, usually referred to as latent and target distributions. Reflow accelerates inference by iteratively straightening the trajectories induced by this vector field. We study the asymptotic behavior of this iteration and characterize its limit points. First, we define weak rectified couplings which always exist. Next, when rectified flow updates are alternated with minibatch optimal transport steps of fixed batch size, we show that any limit is $N$-cyclically monotone, where $N$ is the batch siz...
| Authors | Antonin Chambolle, Johannes Hertrich |
|---|---|
| Primary category | math.PR |
| Published | 7 August 2026 |
| Last updated at source | 7 August 2026 |
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