  We present two Diffusion Monte Carlo (DMC) algorithms for systems of
ultracold quantum gases featuring synthetic spin-orbit interactions. The first
one is a discrete spin generalization of the T- moves spin-orbit DMC, which
provides an upper bound to the fixed-phase energy. The second is a
spin-integrated DMC method which recovers the fixed-phase property by avoiding
the definition of the effective Hamiltonian involved in the T-moves approach.
The latter is a more accurate method but it is restricted to spin-independent
two-body interactions. We report a comparison between both algorithms for
different systems. As a check of the efficiency of both methods, we compare the
DMC energies with results obtained with other numerical methods, finding
agreement between both estimation
