  The generation of large-scale magnetic fields is studied in dilaton
electromagnetism in inflationary cosmology, taking into account the dilaton's
evolution throughout inflation and reheating until it is stabilized with
possible entropy production. It is shown that large-scale magnetic fields with
observationally interesting strength at the present time could be generated if
the conformal invariance of the Maxwell theory is broken through the coupling
between the dilaton and electromagnetic fields in such a way that the resultant
quantum fluctuations in the magnetic field has a nearly scale-invariant
spectrum. If this condition is met, the amplitude of the generated magnetic
field could be sufficiently large even in the case huge amount of entropy is
produced with the dilution factor $\sim 10^{24}$ as the dilaton decays.
