  We study the superconducting instability of a two-dimensional disordered
Fermi liquid weakly coupled to the soft fluctuations associated with proximity
to an Ising-ferromagnetic quantum critical point. We derive interaction-induced
corrections to the Usadel equation governing the superconducting gap function,
and show that diffusion and localization effects drastically modify the
interplay between fermionic incoherence and strong pairing interactions. In
particular, we obtain the phase diagram, and demonstrate that: (i) there is an
intermediate range of disorder strength where superconductivity is enhanced,
eventually followed by a tendency towards the superconductor-insulator
transition at stronger disorder; and (ii) diffusive particle-particle modes
(so-called `Cooperons') acquire anomalous dynamical scaling $z=4$, indicating
strong non-Fermi liquid behavior.
