Sources close to the situation tell TMZ ... Diddy's mom, Janice Combs, and his teenage twin daughters, D'Lila and Jessie, spent time with him last week at the Metropolitan Detention Center.

We're told the four family members went to a visiting area, where they were able to hug and converse ... under supervision by jail staff.

Our sources say this meeting was the first time D'Lila and Jessie were able to see their father since his arrest last month ... and they were very eager to visit him, traveling all the way from their home in California.

We're told the visit was incredibly emotional for everyone ... and after seeing her son, Janice felt compelled to speak out on his behalf, because she felt like he was going through something he didn't deserve.

As we reported ... Janice issued a statement Sunday, saying in part ... "To bear witness to what seems like a public lynching of my son before he has had the opportunity to prove his innocence is a pain too unbearable to put into words."

Janice also said her son is "not the monster they have painted him to be."

Diddy, we're told, has now seen all of his adult children at MDC Brooklyn ... where he's being held as he awaits trial on charges of sex trafficking, kidnapping and racketeering. He's pled not guilty.

Our sources say Diddy is happy his family's all stopped by to see him ... as he's "very family oriented."