  We address the nature of EUV waves through direct observations of the
formation of a diffuse wave driven by the expansion of a coronal mass ejection
(CME) and its subsequent separation from the CME front. The wave and the CME on
2011 June 7 were well observed by Atmospheric Imaging Assembly onboard Solar
Dynamic Observatory. Following the solar eruption onset, marked by the
beginning of the rapid increasing of the CME velocity and the X-ray flux of
accompanying flare, the CME exhibits a strong lateral expansion. During this
impulsive expansion phase, the expansion speed of the CME bubble increases from
100 km s$^{-1}$ to 450 km s$^{-1}$ in only six minutes. An important finding is
that a diffuse wave front starts to separate from the front of the expanding
bubble shortly after the lateral expansion slows down. Also a type-II burst is
formed near the time of the separation. After the separation, two distinct
fronts propagate with different kinematic properties. The diffuse front travels
across the entire solar disk; while the sharp front rises up, forming the CME
ejecta with the diffuse front ahead of it. These observations suggest that the
previously termed EUV wave is a composite phenomenon and driven by the CME
expansion. While the CME expansion is accelerating, the wave front is cospatial
with the CME front, thus the two fronts are indiscernible. Following the end of
the acceleration phase, the wave moves away from the CME front with gradually
an increasing distance between them.
