If you're thinking of the LED Cinema Display, just use a HDMI to mini displayport converter. You'd need a gender changer though (or a converter that accepts a male plug for the output), due to Apple insisting on hardwiring the connector cords to the display, which is ****, TBH.
If you want the Thunderbolt Display, you could theoretically do the same thing, provided it accepts a mini displayport input. It should do that, but this is unconfirmed so treat it as a "no" for now...and you'd lose any Thunderbolt-specific features like all of the built-in ports including USB, the camera, and possibly the speakers as well depending on if they use audio over displayport or USB/thunderbolt.