High fiber! The idea that folks with diverticular disease should avoid seeds, nuts, corn, popcorn has never had any data to support it, so unless a particular food item causes discomfort, i don't advise its avoidance. That said, those with diverticular disease should be on a high fiber diet with plenty of fluid- this has been shown to decrease episodes of pain.
Careful. If you really mean diverticulitis, stay away from any fiber until the diverticulitis has completely reolved, about 4-6 weeks. If you mean diverticulosis, then a good high fiber diet and plenty of fluids in excess of 80 ounces per day not counting caffeine or alcohol is the appropriate regimen to reduce incidence of diverticulitis.