Diddy Parties With Drake Amid Pusha T Beef

Diddy's making his presence known in the fresh beef between Drake and Pusha T ... but it's hard to tell who he's rooting for.

The music and liquor mogul hit up David Grutman's STORY Nightclub in South Beach around 3:45 AM Saturday and joined Drake at his VIP area for some laughs, big hugs, Remy Martin and of course ... several bottles of Diddy's Ciroc vodka.

Drizzy was already at the club, hangin' with Migos, Busta Rhymes and sports stars Le'Veon Bell, Rudy Gay and Lance Stephenson ... shortly after dropping a diss track about Pusha T in response to Pusha shading him on his new Daytona album.

As we reported ... Drake also invoiced Pusha T for $100k for reviving his career.

Pusha's not taking an L yet, though ... because Diddy's got his back, too. He sent the rapper a handwritten letter praising his new album, writing (in cursive, no less) ... "A Modern Day Masterpiece. A Flawless Hip Hop Gem. Classic But Current."

Stay tuned for the latest beef developments.