Probably. Diverticulitis occurs when a small pocket on the wall of the colon ruptures. We used to believe that any foods that can block the small opening of the diverticulum could precipitate diverticulitis, leading to the recommendation to avoid seeded fruits and vegetable and nuts. Nevertheless, no study has substantiated this claim. Therefore, it is probably fine to eat these foods.
In my opinion. Acute diverticulitis where you have an infection, warrants a no fiber diet for 6 weeks to allow the colon to heal. Diverticulosis without an active infection is treated with a high fiber diet, high fluid intake and in spite of recent studies i suggest staying away from nuts, seeds and popcorn. These are small sacrifices in order to avoid a potentially serious complication and emergent surgery.