Bobbi Kristina -- Situation Bleak

Whitney Houston's daughter Bobbi Kristina has "significantly diminished" brain function and doctors have told her family it does not look good ... this according to sources connected with the family.

As we previously reported, the 21-year-old was found face down in her bathtub Saturday and not breathing. She was revived, taken to the hospital where she was placed in a medically-induced coma.

She is currently on a ventilator but we're told tests have determined her brain function is alarmingly low.

Bobbi Kristina's dad, Bobby Brown, is at her bedside.

Doctors have told the family they should continue hoping and praying, but the signs are not good.