The diamond in the video IS NOT MOVING.
The key to the illusion is the thin perimeter of the diamond -
The Perpetual Diamond produces motion continuously and unambiguously in one direction despite never physically changing location. The phenomenon consists of a steady, mid-luminance diamond bordered by four thin edge strips and a surrounding background field. The direction of motion is determined by the relative phases of the luminance modulation between the edge strips and the background. Because the motion is generated entirely by changing contrast signals between the edge strips and background, the stimulus is a valuable tool for tests of spatial contrast, temporal contrast, contrast gain, and color contrast. We demonstrate that observers see motion even when the edge strips subtend only seconds of arc on the retina (which is less than the frequently reported 10 minutes of arc) and that perceived motion is due entirely to changes in the difference in contrast phase modulation, independent from the luminance phase.For a full explanation, go to Neatorama and follow the links there - one of which is an interactive demo.