I think affair or not sounds the same. You won't here I don't love you because I love someone else. It will be other things like you pushed me away, you were emotionally unavailable, you didn't support my dreams, we never were in love.
It's hard to give space when you live together, but just make sure you aren't like a little puppy around her, or kiss butt. You can be kind, cordial, receptive without looking too much like the guy that got kicked to the curb and is desperate to win her back. It's a fine line. Do you have friends that you can go do something fun with? Something that isn't old habits like the bar all night? Catch a show, go play darts or pool. Pull a 180 by going out with friends that doesn't involve drinking. Puttering around the house all the time isn't necessary. You are also allowed to have a life outside home