Nonuniversal correlations in multiple scattering

We show that intensity of a wave created by a source embedded inside a three-dimensional disordered medium exhibits a nonuniversal space-time correlation that depends explicitly on the short-distance properties of disorder, source size, and dynamics of disorder in the immediate neighborhood of the source. This correlation has an infinite spatial range and is long ranged in time. We suggest that a technique of ``diffuse microscopy'' might be developed employing spatially selective sensitivity of the considered correlation to the disorder properties.