In a single word, “no”.
Although there have been several studies that looked at the possibility acne could be caused or worsened by certain foods, it appears that no single food can be represented as an issue amongst acne patients in general. Myths have circulated that junk food or fried food causes acne. This is incorrect. It is certainly not a healthy food choice to eat fast food or fried food but there is no medical study that points to this as a cause of acne. Additionally, there was a study to look at dairy products to determine possible link with acne formation. No direct link could be found. Gluten-free is everywhere, but gluten is a very specific protein that most people can digest. However, there are some people who are truly gluten-sensitive and should avoid gluten for health reasons. If someone has not been tested and found to be gluten-sensitive, I would not encourage anyone and everyone to eliminate gluten from their diet as it can be a very difficult diet to maintain. If in doubt, patients can be tested through an allergist and/or gastroenterologist for gluten sensitivities.
I believe the single best dietary advice to give patients in regards to their acne is this: Drink at least eight 8oz. glasses of plain water each day. We do not get nearly enough water and have likely under-estimated the daily intake requirements for a healthy lifestyle. As Americans, we are likely not getting every necessary nutrient into our diet in a single day. As such, if you do not already take a daily multivitamin, take one. There are so many available, and the industry is not well-regulated (if regulated at all!), however to use a known and trusted brand such Centrum would likely suffice and do a decent if not great job.