I wondered about this question for a long time, but as I walked through repenting for the sins which led to my divorce, I saw something in 2 Corinthians 7 which I hadn't seen before...
10 For the sorrow which is according to the will of God produces a repentance which leaves no regret, leading to salvation, but the sorrow of the world produces death.
When I repented in the right way, the sorrow and regret dissolved and disappeared. The way I understand repentance is that I agree with God that I did something, that it was sinful, and that I need His forgiveness for it. Now when I look back on the things I did wrong, the shame, sting, and ugliness I felt are gone, along with the 'worldly' remorse I had felt. Now I just rejoice in the fact that God led me out of both the sin and the worldly sorrow I had over them.