Relative diffusion coefficients were determined in water for the D, H, and Mu isotopes of atomic hydrogen by measuring their diffusion-limited' spin-exchange rate constants with Ni2+ as a function of temperature. H and D atoms were generated by pulse radiolysis of water and measured by time-resolved pulsed EPR. Mu atoms are detected by muonium spin resonance. To isolate the atomic mass effect from solvent isotope effect, we measured all three spin-exchange rates in 90% D2O. The diffusion depends on the atomic mass, demonstrating breakdown of Stokes-Einstein behavior. The diffusion can be understood using a combination of water "cavity diffusion" and "hopping" mechanisms, as has been proposed in the literature. The H/D isotope effect agrees with previous modeling using ring polymer molecular dynamics. The "quantum swelling" effect on muonium due to its larger de Broglie wavelength does not seem to slow its "hopping" diffusion as much as predicted in previous work. Quantum effects of both the atom mass and the water librations have been modeled using RPMD and a qTIP4P/f quantized flexible water model. These results suggest that the muonium diffusion is very sensitive to the Mu versus water potential used.