Discrete Flow Matching: Convergence Guarantees Under Minimal Assumptions

ArXi:2605.08882v1 Announce Type: new Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution $\mu_1$ from samples drawn from a source distribution $\mu_0$. This framework relies on a fixed coupling between $\mu_0$ and $\mu_1$, and on a deterministic or stochastic bridge to define an interpolating process between the two distributions. The time marginals of this process can then be approximately sampled by estimating the transition rates, or generally the generator, of its Markovian projection.