There's a fair bit of research being done to show that diverticular disease, and other inflammatory bowel diseases are caused by bacterial overgrowth in the large intestine. And what does bacteria feed on??
SUGAR!!
Get rid of the sugar, and the refined flours and grain products. It might be helpful also to avoid dairy products and cheese for a while too, since the small amounts of lactose can be an aggravating factor.
I wrote a brief review of the book "Breaking the Vicious Cycle : Intestinal Health Through Diet", which details the Specific Carbohydrate Diet (SCD), being used successfully for many patients, including Crohn's and ulcerative colitis. You can read it
here. As well, there is a website devoted to the SCD, with up-to-date research, recipes and a message board.
http://www.scdiet.org/
Psyllium husks, and the fiber in salads and vegetables will be helpful, as well there's nuts and their butters, seeds (best to grind them, so they don't get "stuck" in the diverticular out-pouchings) .. flax is wonderful.
Plus losing weight in and of itself will bring relief, since there's less stress and pressure on the abdomen.
Doreen