  We investigate a mechanism to establish ground-state ferromagnetism in
flat-band Hubbard systems based on a kind of {\it order-from-disorder} effect
driven by dispersion. As a paradigm we consider a frustrated diamond chain,
where for ideal diamond geometry the lowest one-electron band is flat, but the
ground state remains paramagnetic for arbitrary on-site repulsion $U$. We focus
on half filling of the flat band. By using numerical and analytical arguments
we present the ground-state phase diagram for a distorted diamond chain, i.e.,
the former flat band becomes dispersive. Driven by the interplay of dispersion
and interaction the ground state is ferromagnetic if the interaction exceeds a
critical value $U_c$.
