Depp definitely has a history of violence and substance abuse, but never of physically abusing a girlfriend prior to Amber Heard making allegations.
However, that doesn't mean the abuse didn't happen. It's common for relationships to become toxic enough or the dynamics different enough that someone commits abuse when he/she hadn't prior to that relationship, and wouldn't after. It should also be noted that Depp was going through some serious financial struggles during his relationship with Heard, and their age difference certainly could have led him to act much differently with Heard than he would have with say, Kate Moss or Winona Ryder.