Big Sean and Ariana Grande were breaking up, they say. Amicably, they say. Well, that really escalated quickly.

Ariana Grande lashed out at Big Sean almost immediately after their breakup by staging Justin Bieber's come-from-behind stage embrace.....so claim sources close to the couple, according to TMZ.

Sources closely connected with them said ... Sean claims it was him who broke off the relationship because she was "immature."

Apparently the downfall of their relationship started in February, when Sean made the most important appearance of his career at the House of Blues in West Hollywood. Everyone showed -- Kanye West, Bieber, JLo, Chris Brown, Jay Z, A$AP Rocky, Tyga, Kylie and Kendall Jenner -- everyone except Ari. According to TMZ, she needed to get ready for the Grammy's the next day, which he reportedly found extremely selfish.

TMZ reports Sean also traveled to see her "10 times more" than she went to see him. He claimed once she demanded that he blow tens of thousands of dollars to take a private jet to see her. Sean, who grew up poor, felt she was a spendthrift ... a sign of immaturity.

But the crowning blow was just after the breakup, apparently. According to TMZ, they were still talking and the door was slightly open for a reconciliation, when Bieber jumped onstage in L.A. and grabbed Ariana from behind. Even though Ariana pushed Biebs away, Sean believes it was all calculated -- NOT by Bieber but Ariana, who apparently are good friends anyway -- to hurt him. Maybe that explains why Sean wasn't as ticked off as everyone had originally believed.