  We follow the trajectories of phase singularities at nulls of intensity in
the speckle pattern of waves transmitted through random media as the frequency
of the incident radiation is scanned in microwave experiments and numerical
simulations. Phase singularities are observed to diffuse with a linear increase
of the square displacement with frequency shift. The product of the diffusion
coefficient of phase singularities in the transmitted speckle pattern and the
photon diffusion coefficient through the random medium is proportional to the
square of the effective sample length. This provides the photon diffusion
coefficient and a method for characterizing the motion of dynamic material
systems.
