Sources connected to the former pair tell TMZ the two eventually "fizzled out" after some time together, no drama or scandal ... it just came to an end. The signs have been on the wall recently that things were likely over ... as each has spent a lot of time in separate cities.

Earlier this week, Tom was spotted in Miami and Irina was in New York. Obviously, it's a quick flight ... but the fact we haven't seen them together is a telling sign.

It was back in July and August when things really heated up between the two -- she spent the night at his place in Los Angeles, got affectionate in his car and even took a trip overseas ... spotted coming out of the same London hotel.

Some started to wonder if Irina had gotten back together with her ex, Bradley Cooper, early last month when she posted a pic of him on social media.

At the time, sources told us Irina and Tom were still together ... and don't forget, she's got a kid with Cooper, so they maintain a level of friendship.

So while Tom and Irina may be donezo, something tells us neither of them will have a problem lining their next partner up ... it's a whole lot easier when you're both rich and really, really good-looking.