flash through (one's) mind
To be thought of in a quick or fleeting fashion. An image of my keys suddenly flashed through my mind, and I remembered where I'd left them.
flash through one's mind
Fig. [for an idea or image] to move quickly through one's mind. (See also flash into one's mind) Suddenly, a great idea flashed through my mind. The same idea flashed through all of our minds at once.