  Given an exact Lagrangian $L$ of an exact symplectic manifold $(M,d\lambda
)$, Cornea and Shelukhin recently introduced a remarkable "cobordism metric"
$d_c$ on the exact Lagrangian cobordism class $\mathcal{L}(L)$ of $L$. In this
note we show that the Liouville flow of $(M,d\lambda )$ induces a flow on
$(\mathcal{L}(L),d_c)$ which expands cobordism distances. In particular we
deduce that $(\mathcal{L}(L),d_c)$ has infinite diameter whenever the Liouville
flow is complete. We also discuss (Hamiltonian and Lagrangian) Hofer-geometric
versions of our result. The proof only uses elementary differential geometry.
