Sources close to the situation tell TMZ Hip Hop Diddy rented out Sei Less NYC for his "Love Album: Off The Grid" release party ... a special occasion seeing as how the restaurant extended its usual midnight shutdown time, so the shindig could go until 4 AM!!!

The moment he entered the bash, Diddy hit up the venue's co-owner Dara Mirjahangiry for a bottle of Ace of Spades, and raised glasses with Yung Miami, Jadakiss, French Montana, Shyne, Jozzy and his sons Quincy and Justin Combs.

We're told the 'Love' album was playing to get the party started, and once the shots from Diddy's DeLeon Tequila began to flow ... they launched into an impromptu karaoke session.

Keyshia Cole led the sing-along to her classic "Love" track and Diddy commanded The Notorious B.I.G.'s "Warning" for the crowd.

Fans have been rallying around the R&B compilation, and its lead-off music vid also dropped on Friday ... "Another One of Me" featuring French, 21 Savage and The Weeknd in his final appearance with that stage name.