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(Joint work with J. Palmer) ÌýSuppose that $\phi_t: L \to X, t \in [0,T]$Ìýis a family of Lagrangian immersions flowing under a Maslov flow such as a reverse mean curvature flow, or reverse mean curvature flow coupled to a K\"ahler-Ricci flow as introcuded by Smoczyk. ÌýIf $\phi_0$ is weakly unobstructed then so is $\phi_T$ and $HF(\phi_0) \cong HF(\phi_T)$. ÌýThis is part of a conjecture of Joyce, Ìýand related to the speaker's Lagrangian minimal model program.