You either forgive and rebuild your relationship from the ground up again, or you walk away, start again when you are ready with someone who has never harmed you.
If the relationship is less than a few years old and there are no children, then walk away. It will take honesty and years of hard work to rebuild a solid relationship and it will not be possible for everyone to achieve this. It will be easier to invest years of hard work into a brand new relationship than one that is only 18 months old with a cheater.
Once you have worked through all the issues that led up to the cheating, the details of the cheating and the steps taken to insure that it will not happen again, together with a counsellor - then you will not need to hold the cheating over the other persons head. If you can't imagine this outcome then leave now.
If you feel you need to randomly argue with you partner, then leave now.