  We consider the spin-orbit-induced spin Hall effect and spin swapping in
diffusive superconductors. By employing the non-equilibrium Keldysh Green's
function technique in the quasiclassical approximation, we derive coupled
transport equations for the spectral spin and particle distributions and for
the energy density in the elastic scattering regime. We compute four
contributions to the spin Hall conductivity, namely, skew scattering,
side-jump, anomalous velocity, and the Yafet contribution. The reduced density
of states in the superconductor causes a renormalization of the spin Hall
angle. We demonstrate that all four of these contributions to the spin Hall
conductivity are renormalized in the same way in the superconducting state. In
its simplest manifestation, spin swapping transforms a primary spin current
into a secondary spin current with swapped current and polarization directions.
We find that the spin-swapping coefficient is not explicitly but only
implicitly affected by superconducting correlations through the renormalized
diffusion coefficients. We discuss experimental consequences for measurements
of the (inverse) spin Hall effect and spin swapping in four-terminal
geometries. In our geometry, below the superconducting transition temperature,
the spin-swapping signal is increased an order of magnitude while changes in
the (inverse) spin Hall signal are moderate.
