A noteworthy study was reported in a NYTimes article describing the impact of weight loss in a group of obese patients with psoriasis. The weight loss intervention was unfortunately the standard low-calorie approach, rather than a truly anti-inflammatory diet, but it most certainly reduced sugars and other processed foods as we would hope to do to calm down immune-related inflammation. The folks who lost weight (34 pounds more, on average, than the non-dieters) reported improvement in both their skin and their overall quality of life.
You might have read the article on osteoarthritis, also on this site, where I mentioned that losing weight helps with arthritis symptoms - not just because the arthritic patient is carrying less weight, but specifically because they are carrying less inflammatory fat tissue. Adipose (fat) tissue adds a hefty dose of inflammatory molecules to the circulation and can contribute to inflammatory flares, whether in the joints or, as this article describes, on the skin.
Ideally, for patients with inflammatory skin conditions, they would be counseled to address all dietary sources of inflammation. High on the list would be the sugars and processed foods these dieters probably avoided (standard low-calorie advice), but I would also suggest that they spend at least a month or two avoiding all grains, legumes, and dairy, as recommended in the Paleo Diet. Other foods to avoid, and particular nutrient needs, would have to be addressed on an individual basis.
