Diane Keaton Has Been Cremated, Days After Dying From Pneumonia Infection

12:20 PM PT -- It appears Diane began seeing the doctor September 24th and last saw her doctor on Thursday, October 9th. She was pronounced dead on Saturday, October 11th.

Diane Keaton has been cremated ... and her death certificate backs up what her family said ... that she died from pneumonia ... and there were no other significant contributing factors.

In the death certificate, obtained by TMZ, the official cause of death is listed as primary bacterial pneumonia.

The document also says Diane died Saturday and was cremated Tuesday.

PEOPLE was the first to report on the details of the death certificate.

As we first told you, a longtime friend said they weren't shocked by Diane's death because she had been struggling for a while with an illness.

The L.A. Fire Department responded to Diane's home around 8:08 AM Saturday and transported one person -- confirmed by sources as Keaton -- by ambulance to a nearby hospital.

Dispatch audio from the call to service featured first responders reporting a "person down" at Diane's address.

Diane's friends in Hollywood have posted a ton of tributes to her ... and her former romantic partner Woody Allen said, "When we first met, I thought she was so charming, so beautiful, so magical, that I questioned my sanity."