Recently we observed a strong reduction of spatial coherence of the emission of large-aperture vertical-cavity surface-emitting lasers when they are driven by microsecond electrical pulses [Opt. Express 13, 9337 (2005)]. We study the influence of this partial spatial coherence on the propagation characteristics. The spatial decoherence manifests itself in the formation of a Gaussian far-field intensity distribution. We measure the transverse pulse profile from near to far field and see that the shape-invariant far-field regime starts after 140 microm in the pulsed regime as opposed to several centimeters in continuous wave operation. This value matches quantitatively calculations made with a novel partially coherent propagation model without any free fitting parameters.