Within the range of validity of the stationary diffusion equation, an ideal diffusive-light invisibility cloak can make an arbitrary macroscopic object hidden inside of the cloak indistinguishable from the surroundings for all colors, polarizations, and directions of incident visible light. However, the diffusion equation for light is an approximation which becomes exact only in the limit of small coherence length. Thus, one expects that the cloak can be revealed by illumination with coherent light. The experiments presented here show that the cloaks are robust in the limit of large coherence length but can be revealed by analysis of the speckle patterns under illumination with partially coherent light. Experiments on cylindrical core-shell cloaks and corresponding theory are in good agreement.