Diddy‘s 4 children with Kim Porter are fed up with conspiracy theories and online rumors suggesting their father had anything to do with their mother’s tragic death.

Sons Quincy and Christian, and twin daughters Jessie and D’Lila took the extraordinary step Tuesday night to address what they call “hurtful and false rumors” about their parents’ relationship.

In a joint statement, they say it’s been hard to reconcile how their mom Kim was taken from them too soon, but they quickly dismiss any unfounded or unproven theories Diddy was involved in her death … writing, “The cause of her death has long been established. There was no foul play.”

Remember, Kim died suddenly in 2018, and an autopsy revealed her cause of death to be pneumonia. However, in the wake of Diddy’s arrest and federal indictment, some people — fans and even Christian’s estranged biological father, Al B. Sure! — have called for Kim’s death investigation to be reopened.

Al straight up said this week he thinks Kim was murdered … a theory he tied to a new book — called “Kim’s Lost Words: A Journey for Justice From the Other Side” — allegedly containing Kim’s journal entries from the time she was with Diddy.

Kim and Diddy’s kids, though, say the book’s claim of authenticity is BS. As they put it, “Claims that our mom wrote a book are simply untrue. She did not and anyone claiming to have a manuscript is misrepresenting themselves.”

They add, “We are deeply saddened that the world has made a spectacle of what has been the most tragic event of our lives.”

In addition to asking for privacy, the kids don’t want “horrific conspiracy theories” tearing down their mother’s legacy as they “continue to cope with her loss every day.”

TMZ broke the story … all of Diddy’s children remain supportive of him as he sits in jail awaiting his federal trial. In addition to the 4 kids with Kim, Diddy also has Justin and baby Love with 2 other women. Although, Quincy is not his biological son, Diddy did adopt him.