For me publicity and public relations are totally hand in hand.  So while the saying is "there is no such thing as bad publicity," I feel the same can be said about public relations.  As long as people are discussing you in some capacity that is a win.  The challenging part is shifting negative PR into positive PR that you can benefit from.  A lot of different things factor into this.  While I almost hate to bring him up because he's been discussed to often, I feel Chris Brown is a perfect example of a reputation on the mend.  As a celebrity, image is everything, he ruined his reputation after his incident with ex girlfriend Rihanna three years ago.  He has be able to salvage his career because he is truly talented.  People will always bring up what happened because that is human nature but you can't deny his talent.  Initially, he went on a media tour doing interviews apologizing it wasn't until his tribute to Michael Jackson when people actually began to think he showed genuine remorse.  That moment began to shift bad PR to good PR.  He was able to begin that through talent.  Sometimes it isn't that easy.  Sometimes you have to be seen in public doing things for others.  Otherwise known as PR stunts.  Like i said it all depends.  Others have not been as fortune as Chris Brown.  Mel Gibson could be a great example for this.  He had one racist rant too many and i believe people are tired of that.  He would need to do something more than apologize like he's been doing.  He needs a better PR team to accomplish this.  A good PR team is essential in imaging.  We will all make mistakes but in order to remain successful you will need public relations to mold you.