Is Iran causing the turmoil in Iraq?

We all know that Iran is Shiite and Saddam's Iraq is mainly Sunni. Iraq defeated Iran in most of their skirmishes. Now that Saddam is dead, may it be that Shiites are itching to take revenge against their former oppressors, the Sunnis? And, does Iran have active participatiuon in the current turmoils in Iraq like training the Shiite insurgents, providing weapons, and giving surveillance infos? Take note that 3 days ago, an Iranian spy drone was shot down by US planes under Iraqi territiory...