  We derive and evaluate one-loop functional flow equations for the effective
interactions, self-energy and gap function in spin-singlet superfluids. The
flow is generated by a fermionic frequency cutoff, which is supplemented by an
external pairing field to treat divergencies associated with the Goldstone
boson. To parametrize the singular momentum and frequency dependences of the
effective interactions, the Nambu interaction vertex is decomposed in charge,
magnetic, and normal and anomalous pairing channels. The one-loop flow solves
reduced (mean-field) models for superfluidity exactly, and captures also
important fluctuation effects. The Ward identity from charge conservation is
generally violated, but can be enforced by projecting the flow. Applying the
general formalism to the two-dimensional attractive Hubbard model, we obtain
detailed results on the momentum and frequency dependences of the effective
interactions for weak and moderate bare interactions. The gap is reduced by
fluctuations, with a stronger reduction at weaker interactions, as expected.
