We determine the effect of replacing geometrical ray theory in surface wave tomography with scattering theory. We describe a tomographic method based on a simplified version of the scattering sensitivity kernels that emerge from the Born or Rytov approximations in which surface wave travel times are a weighted average of phase or group slowness over the first Fresnel zone of the wave. We apply this diffraction tomography to Rayleigh and Love wave group velocity measurements to produce group velocity maps from 20 to 150 s period on a 2¿ ¿ 2¿ grid globally. Using identical data and damping parameters, we also produce maps using Gaussian tomography which is based on ray theory with intuitive Gaussian smoothing constraints. Significant differences in the amplitude and geometry of the imaged features appear primarily at long periods but exist even in the short-period maps in regions where average path lengths are large. Diffraction tomography, therefore, is significant in most oceanic regions at all periods, but it is also important on continents at long periods at least. On average, diffraction tomography produces larger velocity anomalies in a period-dependent band of spherical harmonic degrees, and diffraction and Gaussian tomography maps decorrelate past a critical spherical harmonic degree that also depends on period. The widths of resolving kernels that emerge from diffraction tomography are systematically larger than those from Gaussian tomography. Finally, mantle features inferred from diffraction tomography tend to have larger amplitudes and extend deeper than those from Gaussian tomography.