Sources close to the former couple tell TMZ ... while they have been trying to work things out for the past few months, they've officially broken up following their initial split back in the early days of the coronavirus shutdowns.

As you'll recall ... Scott entered rehab not long after they went bike-riding together on the beach in April, and then there were other signs they were on the outs.

Mainly, Sofia was hanging out with another guy in mid-May -- just days after Scott's brief rehab stint -- and rumors began to circulate she was dating other people.

However, our sources say she was the one really pushing to get back together with Scott ... it just didn't happen. We're told Scott recently called it off definitively, and they're no longer on speaking terms.

As for what led to the breakup ... our sources say the 15-year age difference became a growing source of friction, as well as Scott's family commitments. We're told he's also seeking a quieter lifestyle to focus on his business ventures ... and it didn't mesh well with Sofia's life.

Our sources say Scott was very clear in his decision that this is it -- he doesn't see them getting back together. We'll see.