The cycle of avoidance then craving is well known, but I don't personally think just going at it and keeping eating processed stuff is the answer.
We don't advise people to do this with smoking, we just usually encourage them to go either cold turkey or use patches, etc.
I ended my affair with processed food by accident. We got into watching some videos online last year about the industry and associated illnesses, especially how since the introduction of hydrogenated oils into foods (they replaced butter) has created more issues than we can care to let on. How such substances, along with processed sugars can reprogram our bodies to behave abnormally.
So whilst not interested in dieting or losing weight, we lost a fuck ton as a consequence of being 'put off' that stuff after seeing it in a new light.
I think education is the key - instead of perceiving processed foods as delicious and naughty, it might be better if we saw them for what they were, ie, mostly poison. It could sound pompous, but it really put us off. We got inot buying from scratch, which even turned out cheaper, escept for my thing with pine nuts (!!). It is much more expensive to switch to good quality meant though. Recipes found online are easy and cost effective, and it is amazing how many of the homemade things taste even better than the stuff doused in palm oil, sugar and shit.
My post sounds so sanctimonious but it is hard to talk online due to there being no tone or facial expressions, so please know that was not intended! 
I think you just have to come to see it as poison, like you would a cigarette, or else it is a lifetime of craving.