Nicole Kidman and Keith Urban are each keeping busy as their divorce continues to make headlines … both making separate public appearances this weekend.

Kidman stepped out in Dallas on Saturday night to support a cause close to her heart — attending amfAR’s charity auction, which raises funds for AIDS research and HIV prevention worldwide. The Oscar winner was all smiles as she appeared on stage to speak at the event.

Meanwhile, her estranged husband hit the stage on the East Coast … performing in Bristow, Virginia as part of his ongoing High and Alive World Tour. Urban put on a high-energy show for thousands of fans, marking another stop in his string of performances since news of the couple’s divorce broke.

We broke the story … Nicole and Keith separated this summer — Keith’s idea, Nicole wanted to make the marriage work — and, they’ve been living in separate Nashville homes for the past few months. Our sources say they think Keith’s going through a midlife crisis.