9:11 AM PT -- 1/24 -- Brown just literally ran out of jail after he bonded out ... and the clip is pretty hilarious.
The 31-year-old bolted down the stairs and went into a full-on sprint when he hit the parking lot ... but it turns out, he was running the wrong way and had to double back.
Antonio didn't talk with reporters as we he was leaving ... but his attorney said for him, "We will be speaking soon."
6:34 AM PT -- 1/24 -- Sources tell us AB has already been in contact with bail bondsman Ira Judelson -- who seems to be the go-to guy for the rich and famous.