Philip Seymour Hoffman's funeral has just begun -- and the church is jam-packed with the late actor's famous friends ... including Cate Blanchett, Spike Lee, Louis C.K., Ethan Hawke, and Ellen Burstyn.

The private funeral service for family and friends is now underway at the Church of St. Ignatius Loyola in NYC -- the same church where Jackie Kennedy Onassis and Aaliyah's funerals were held.

All told, roughly 400 people were expected to attend the ceremony.

As we reported, 46-year-old Hoffman was found dead Sunday from an apparent heroin overdose. He is survived by his longtime partner Mimi O'Donnell and 3 young children.

A larger memorial service is in the works for later this month.