Are there different types of diverticulitis cures?

No. While there are many different antibiotics that can be used to treat diverticulitis, and taking a regular fiber supplement may reduce the likelihood of further episodes, the only cure for diverticulitis is to remove the diseased portion of the colon. This is commonly done as a laparoscopic operation. It represents major surgery and is only indicated under certain circumstances.
Cures=NO. Different treatments exist, but no cure. Diverticulitis is an infection, treated with either IV or oral antibiotics, and then dietary changes afterwards to prevent future attacks, but you will always have diverticuli forever, unless surgically removed for appropriate reasons (only in about 10% of all people with diverticulitis).