We propose a novel formulation of the generalized cross correlation with phase transform (GCC-PHAT) for a pair of microphones in diffuse sound field. This formulation elucidates the links between the microphone distances and the GCC-PHAT output. Hence, it leads to a new model that enables estimation of the pairwise distances by optimizing over the distances best matching the GCC-PHAT observations. Furthermore, the relation of this model to the coherence function is elaborated along with the dependency on the signal bandwidth. The experiments conducted on real data recordings demonstrate the theories and support the effectiveness of the proposed method.