That the speed of light in vacuum is constant is a cornerstone of modern physics. However, recent experiments have shown that when the light field is confined in the transverse plane, the observed propagation speed of the light is reduced. This effect is a consequence of the transverse structure which reduces the component of wavevector of the light in the direction of propagation, thereby modifying both the phase and group velocity. Here, we consider the case of optical speckle, which has a random transverse distribution and is ubiquitous with scales ranging from the microscopic to the astronomical. We numerically investigate the plane-to-plane propagation speed of the optical speckle by using the method of angular spectrum analysis. For a general diffuser with Gaussian scattering over an angular range of 5°, we calculate the slowing of the propagation speed of the optical speckle to be on the order of 1% of the free-space speed, resulting in a significantly higher temporal delay compared to the Bessel and Laguerre–Gaussian beams considered previously. Our results have implications for studying optical speckle in both laboratory and astronomical settings.