The music mogul started crying during an interview with Essence while opening up about the pain he's anticipating this weekend on Mother's Day ... his first without the mother of his 3 kids.

Diddy says he and his children will celebrate Kim on Mother's Day, but it's still gonna hurt ... because he still hasn't gotten over her death. Diddy acknowledges it's gonna take some time to heal, if he ever does.

TMZ broke the story ... Kim died unexpectedly back in November at the age of 47, losing her battle with pneumonia. Diddy was distraught for weeks, calling her death a nightmare, and delivering a powerful eulogy at Kim's funeral.

When we last saw Diddy, he told us he was trying to soldier on and take care of his kids without Kim ... but it's clear her loss still weighs heavily on him.