Are Ashton Kutcher and Demi Moore splitting?

(CBS) Are Ashton Kutcher and Demi Moore heading for divorce?

Rumors are swirling about the couple's marriage amid tabloid reports that the new "Two and a Half Men" star was unfaithful.

Pictures: Ashton Kutcher
Pictures: Ashton and Demi

Star magazine, citing "a source close to the pair," claims that Kutcher and Moore have separated and that the marriage ended because of Kutcher's "serial cheating." The Daily Mail also has photos of a woman who claims she had a "fling" with the actor last weekend, when he and Moore spent their sixth wedding anniversary apart.

Both Kutcher, 33, and Moore, 48, have kept mum on the rumors, save for a pair of potentially telling messages on their Twitter pages.

Early Thursday morning, Kutcher posted a link, without comment, to the Public Enemy song "Don't Believe the Hype." And on Sept. 23 - the day before the couple's anniversary - Moore shared a quote from the Greek philosopher Epictetus: "When we are offended at any man's fault, turn to yourself & study your own failings. Then you will forget your anger."

Moore and Kutcher began dating in 2003 and married in 2005. So far, reps for the actors have not commented.