Place a utility knife at the top edge of the molding and pull it along the entire length to cut through any paint or caulk that has sealed it to the wall. Repeat the process on the bottom side of the molding. Walk to the corner and draw the blade down the vertical seam to free it as well.
Kneel down so you can closely examine the corner molding. Look at the center of the corner where the two pieces of molding meet and determine which section of molding is on the top. This is the piece where you can see the visible free edge. The other piece of molding fits underneath the top portion.
Insert a pry bar under the identified piece of molding, spacing it four to five inches from the corner. Pull back gently on the handle of the pry bar, just until you see the molding lift from the wall. Do not try to pull it all the way off since this can crack it.
Slide the pry bar under the loosened molding toward the corner. Pry up on the molding again and the top section of the corner molding will come free. Work your way in the opposite direction to remove the remainder of the partially loose molding in the same way.
Return to the corner where the remaining molding is still installed. Insert the pry bar under the inside corner of the molding and pry up until it comes free from the wall. Work your way down the length of the molding to remove it from the wall.