  We microscopically derive the spin diffusion equation in an s-wave
superconductor in the vicinity of the superconducting transition temperature
Tc. Applying the general relation between the relaxation function and the
response function to the present spin diffusion problem, we examine how the
spin relaxation time and the spin diffusion coefficient are renormalized in the
superconducting state. The analysis reveals that, below Tc, both the spin
relaxation time and the spin diffusion coefficient are increased, resulting in
an enhancement of the spin diffusion length. The present result may provide an
explanation for the recent observation of an enhanced spin pumping signal below
Tc in a Py/Nb/Pt system that is free from the coherence peak effect.
