The grapple rules are silent on the matter, but the movement/AoO rules say, "Moving out of a threatened square usually provokes an attack of opportunity from the threatening opponent. There are two common methods of avoiding such an attack—the 5-foot-step and the withdraw action (see below)."
This movement out of a grapple is neither a 5-foot-step nor a withdraw action. Depending on your DM, it might be considered "part of normal movement" for the purposes of using Tumble to avoid that AoO.
If I were the DM, I'd give the guy an AoO unless the escapee could Tumble to avoid it. But I'm pretty generous with what I consider "part of normal movement." I figure as long as it doesn't involve Metamucil, Beecham's Pills, or Blackmores Colon Care, it's pretty normal.