We have used the linear optical diffraction method to study the diffusion of hydrogen atoms on flat and stepped W(100) surfaces. At 0.17-monolayer (ML) H coverage, the diffusion coefficient (D) shows a strong anomalous dip at the substrate reconstructive phase transition temperature in an Arrhenius plot for diffusion on both surfaces. No anomalous diffusion behavior is observed at 1.2-ML H coverage on both surfaces in the entire range studied, 240-380 K, consistent with the absence of the phase transition at this H coverage. The strong reduction of D can be attributed to the diverging friction damping near the transition. Steps do not suppress the substrate phase transition and affect the diffusion anomaly very little. For both H coverages, the only effect of steps is to introduce a small Schwoebel-Ehrlich barrier (∼2.2 kcal/mol for 1.2 ML and ∼2.8 kcal/mol for 0.17 ML) near the step edges, which slows down H diffusion perpendicular to steps. Measurements of H diffusion parallel to steps reveals no obvious enhancement due to step edge diffusion.