Do you believe that abusive partners can change?

I was engaged to a wonderful man a while back, and eventually broke it off because there were a lot of problems on both sides of the relationship.
One was that he was physically abusive- I was never seriously hurt but I was slapped, bit, etc. Although it
is not an excuse, he was also sick and not on meds at the time.
We were apart for a while and it was very hard. We are back together now and he is so different. He is so sorry for his actions and we are both better after the break up we experienced. We have talked about it a lot and I think he has changed.
I do not feel like he will hurt me again (if he did- no chances, I'd leave asap). We are so in love and I genuinely feel that he has changed. Even if he accidentally snaps at me- he catches himself and apologizes. We just got back together but at this point it seems that he has changed. My friends call me stupid but I was supposed to marry this man and if he is not hurting me and we are in a healthy relationship now I do not see a problem. We make eachother so happy.
Do you think that abusive partners can change?