We present two diffusion Monte Carlo (DMC) algorithms for systems of ultracold quantum gases featuring synthetic spin-orbit interactions. The first one is a spin-integrated DMC method which provides fixed-phase energy estimates. The second one is a discrete spin generalisation of the T-moves spin-orbit DMC [Melton et al., J. Chem. Phys. 144, 244113 (2016)], which provides an upper bound to the fixed-phase energy. The former 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 estimations.

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