Sources connected to the former couple tell TMZ ... there was no cheating or fighting involved in Miley's decision to break things off after a 2-month whirlwind romance where she and Kaitlynn were practically inseparable.

We're told the two women "got along like a house on fire," and before long they were living together ... and there was even talk of marriage.

However ... as things got increasingly hot and heavy, our sources say Miley realized she wasn't ready to hop back into another committed relationship so soon.

Despite the breakup, we're told Kaitlynn's still on good terms with Miley ... and she's not bothered by her apparent new fling with Cody Simpson. However, we're told Kaitlynn has expressed concern over Miley's behavior to friends ... and she's worried for her well-being.

As we reported ... Miley and Kaitlynn were first linked when they were spotted kissing poolside in Italy on the heels of Cyrus announcing she'd separated from her husband, Liam Hemsworth. Carter herself had just split with her man, Brody Jenner.