This article on Reuter's claims that the source of acne is Western Culture.
The article says that the investigators looked at two non-Westernized cultures and found that they had no incidences of acne. The authors decided it was because of the food the cultures eat.
I think it much more likely to have to do with the genetics of the three groups. The Islanders and the hunter-gatherers have inter-married for generations, perhaps centuries. They all share the same gene bank. Their particular gene bank is not a carrier for acne. Western cultures have all inter-married and if we once had non-acne gene banks, they must have been recessive, for most of us still have acne.
But, if you want to give up food to see if it will cure your acne, the article identified cereals, sugars, bread, pasta, and refined foods as the problem. So if you eat all your food as it came from the source, fresh and un-processed, you have a chance, the article says, of getting rid of your acne.