  We present the first systematic study of the stellar populations of
ultra-diffuse galaxies (UDGs) in the field, integrating the large area search
and characterization of UDGs by the SMUDGes survey with the twelve-band optical
photometry of the S-PLUS survey. Based on Bayesian modeling of the optical
colors of UDGs, we determine the ages, metallicities and stellar masses of 100
UDGs distributed in an area of $\sim 330$ deg$^2$ in the Stripe 82 region. We
find that the stellar masses and metallicities of field UDGs are similar to
those observed in clusters and follow the trends previously defined in studies
of dwarf and giant galaxies. However, field UDGs have younger
luminosity-weighted ages than do UDGs in clusters. We interpret this result to
mean that field UDGs have more extended star formation histories, including
some that continue to form stars at low levels to the present time. Finally, we
examine stellar population scaling relations that show that UDGs are, as a
population, similar to other low-surface brightness galaxies.
