The Paleolithic diet and the Anti-Inflammatory diet are very similar. The Paleo diet is a type of anti-inflammatory diet. It is designed to reduce the body's inflammation and help your body be at its healthiest. That is also the purpose of the Anti-Inflammatory diet.
The doctor associated with the Anti-Inflammatory diet is Dr. Weil. I own two different anti-inflammatory diet books, neither by this doctor but they are nearly identical. There is actually a class that teaches you the ins and outs of the anti-inflammatory diet from the University of Arizona. Dr. Weil is one of the faculty for this class, and you can take it online. Here's the link to the class if you are interested: http://integrativemedicine.arizona.edu/online_courses/anti_inflammatory.html
The primary difference between the paleo diet and the anti-inflammatory diet is their view on meat and legumes. Paleo says okay for any lean meat, while the anti-inflammatory diet is more restrictive. In the anti-inflammatory diet, they say no red meat. Paleo does not include any type of legumes in that diet, while the anti-inflammatory diet says you can eat certain legumes and encourages you to eat them.
Both diets agree that processed foods are detrimental to your health and that you should avoid grains like bread and pasta. (One of my books says it is okay to eat grains as long as they are whole grains, while my other book says that wheat should not be eaten.) I'm not sure about Paleo's view of these grains, but the anti-inflammatory diet allows for you to eat grains like quinoa, amaranth, farro, and a couple other types of grains.
I hope this helped you out. From personal experience, I can say that this diet has helped me get my lupus under control and I think it would greatly help anyone who deals with inflammation.