Profiling structured beams produced by X-ray free-electron lasers (FELs) is crucial to both maximizing signal intensity for weakly scattering targets and interpreting their scattering patterns. Earlier ablative imprint studies describe how to infer the X-ray beam profile from the damage that an attenuated beam inflicts on a substrate. However, the beams in-situ profile is not directly accessible with imprint studies because the damage profile could be different from the actual beam profile. On the other hand, although a Shack-Hartmann sensor is capable of in-situ profiling, its lenses may be quickly damaged at the intense focus of hard X-ray FEL beams. We describe a new approach that probes the in-situ morphology of the intense FEL focus. By studying the translations in diffraction patterns from an ensemble of randomly injected sub-micron latex spheres, we were able to determine the non-Gaussian nature of the intense FEL beam at the Linac Coherent Light Source (SLAC National Laboratory) near the FEL focus. We discuss an experimental application of such a beam-profiling technique, and the limitations we need to overcome before it can be widely applied.