The diffusion of H-1 and H-2 on the (001) plane of a tungsten field emitter has been studied by the field emission fluctuation method, employing a rectangular probe for anisotropy determinations. Diffusion was found to be temperature independent for T < 140 K, followed by a slightly activated regime between 140 and 220 K. In this range E = 1-2 kcal/mol and D-0 = 10(-9)-10(-10) cm(2)/s. For T > 220 K a third regime with E = 4-7 kcal/mol and D-0 =10(-5)-10(-7) cm(2)/s occurs. There is some diffusion anisotropy for both tunneling and weakly activated diffusion, and also for high temperature diffusion at very low coverage, presumably corresponding to surface reconstruction with a single domain predominating. For T < 200 K evidence for the coexistence of two diffusion regimes was found and is tentatively attributed to fluctuations caused by single atoms and by collective modes, respectively. Isotope effects were small under all conditions, including tunneling. Mean square fluctuations were temperature dependent, except below 140 K. The resultant ''activation'' energies suggest that much of this dependence involves substrate compression. The small isotope effect in tunneling and the small values of E and D-0 in the first activated regime are attributed to the involvement of substrate distortions in diffusion, essentially via polaronic effects and adsorbate-substrate atom phasing requirements for H hopping. The self diffusion of thermally generated W atoms at 660 less than or equal to T less than or equal to 775 K was also investigated: E approximate to 18 kcal/mol and D-0 approximate to 10(-7) cm(2)/s.