It's a complicated theory, and I actually developed this theory not because I was looking for an explanation of pimples, but of atherosclerosis, and I found out they are caused by the same thing: Dying phagocytes. In short, intestinal bacteria tries to enter the body through the gut lining, phagocytes kill them, and the dead phagocytes in this ongoing intestinal war either end up in atherosclerotic lesions or pimples.

I'm not going to explain the entire theory here, if you guys want to know the entire theory, I can post a link to my original thread that discusses it (Or I can copy and paste it here).

In short, to treat acne through diet:

Eliminate all sources of sucrose/fructose [Candy, chocolate, sweets, smoothies, basically anything sweet. Even fruits.]; intestinal bacteria grows like gang busters off these two.

Eliminate all sources of 'dirty food' [think dark meats, rotten food and the like]

Eliminate wheat and other gluten products(Like Rye and Barley) [The gliadin protein in the wheat increases intestinal permeability which essentially opens the gates to your body to the invading bacteria]

For acne in particular, I would suggest eliminating dairy. Don't really understand it's bacterial connection, but I do know it boosts blood sugar levels (insulinotropic), which itself probably helps boost the invading bacterial populations. And, I notice I get pimples if I consume a lot of dairy.

For suggested food groups. Anything that helps keep the intestine clean, like garlic, cocoa, coffee, wine, vinegar, pungent citrus fruits[lemons/limes], fermented foods, really, most any pungent sharp/acidic food.

For replacement carbs(for wheat), there's plenty of options (I'm going to list what I think are the healthier options first). Maize (Non-sweet corn, has more glucose than sucrose), Sweet potatos, Peas, Cassava, Carrots and then among grass seeds: Quinoa, Rice(Brown and white), Millet, Oats, etc. [Oats do not contain gliadin and do /not/ increase intestinal permeability. But, I would advise watching portion sizes because of its high GI.]. I personally prefer the vegetable carbs over the grass seed carbs, they have less controversy over their builtin protections(potentially harmful to humans)[such as saponins, goitrogens, phytates, etc.] and some of the longest living cultures historically consumed vegetable carbs. Maize in South America, Sweet Potatos in Okinawa, Cassava in Africa, etc. They also have nutrients that white rice doesn't have, and doesn't take forever to boil like brown rice. They also usually don't need to be rinsed like grains /should be/, though if you picked them fresh from the field, I'd recommend rinsing the dirt off, lol. Boiled vegetables also usually have a lower GI than white rice/oats, potentially lowering diabetes risk and leaving you fuller longer. They also tend to have plenty of important vitamins and minerals, like potassium (And if farms fully restored the mineral content to the soil, they would also be rich in magnesium.)

Update: I also forgot to mention Eggs. I believe raw eggs have strong antibiotic properties (The albumin is supposed to nourish and protect the yolk), and eggs definitely seem to help lower and stabilize blood sugar levels when consumed in a meal (raw or not) [I believe keeping blood sugar levels in check probably helps keep invading bacterial populations down. Diabetics seem to have a problem with infections. Regular exercise and strength training also helps suppress and regulate blood sugar levels.]. I've noticed so many people who live superlong lives consume eggs, even that one guy whose cats lived to 32 or some such.

I speculate the reason why the phagocytes don't filter through the kidney and out the urine is because the phagocytes are too large (They'd end up sticking to the kidney's filters, which it appears some of them do, probably leading to kidney failure in some people.), so they need to go through something a bit more 'open'; your pores. Why some of the dead phagocytes stick to the vessel walls in the form of arthersclerosis is a mystery to me; perhaps the body doesn't really know it's detrimental, since it's usually harmelss in the short-term /until/ it becomes too advanced in the longterm. Perhaps there's evolutionary reasons I could speculate about. Maybe it needs to cement the bacteria down right away to prevent it escaping and potentially risking sepsis.