In a non-infidelity example, I did something pretty shitty to my wife many years ago.
As she was 7 months pregnant with our second child(and a three year old toddler), and being high risk due to a hereditary heart condition, I went on a snowmobiling trip 3/4 of the way across the country. She didn't beg me to stay, clinging to my leg as I walked out the door, but she wasn't real happy about it either. I mean, looking back, I have to ask what the hell was running through my head?
Needless to say, when I came home, it was to an empty house(no cell phone). She was already hospitalized, and our three year old was with his aunt. It was several more days until she was released.
Now, I can try to make some lame excuses about how I was young, and I didn't really comprehend the severity of the whole situation. I was old enough to be married with children, and me putting my wants first, in this case, had terrible results. The bottom line is, I have never asked for forgiveness for this, what should be called, betrayal. How could I? Why should I? What I should be doing in that situation is to to learn from that experience, and make new boundaries that will never put her, or my children, in that situation again.
Let's fast forward 25+ years. I don't think that she has forgiven me for this, nor do I feel that she should have to. That is for her to decide. But I also don't believe that she has had to hold back intimacy, or put up....and keep up....emotional walls. I did her wrong, and feel like I have tried to make amends.....but I don't feel that she has to forgive me for us to have a better marriage. I apply the same to her cheating. If she has made continuous life-changing efforts to try to atone for what she did, I can recognize that, and base my intimacy on her efforts. Even if I don't forgive her(which is my issue alone at this point), I believe the reconciliation can continue without resentments/holdbacks/emotional walls that would remain unchanged with forgiveness.....in my opinion.