Is there any conclusive study relating the food consumed and the occurrence of acne?
The short and unsatisfying answer is no-- it remains controversial due to lack of high quality randomized clinical trials. According to an article in UptoDate, a reliable resource for many physicians, last updated September 2014, there is an association between acne and intake of milk in which milk components could exacerbate acne. Unfortunately, there have been no randomized clinical trials on this subject. According to the same article, "there is no reliable evidence that ingestion of chocolate is associated with an increased prevalence or severity of acne." In a similar light, the article continues on to say that "data on favorable effects of dietary factors such as zinc, omega-3 fatty acids, antioxidants, vitamin A, and dietary fiber on acne vulgaris are limited. Further studies are necessary to determine the roles of these supplements in acne vulgaris."  

Reference: 


http://www.uptodate.com/contents/pathogenesis-clinical-manifestations-and-diagnosis-of-acne-vulgaris?source=search_result&amp;search=acne+and+food&amp;selectedTitle=1%7E150#H8