“Marriage is one of the most difficult things in the world and unfortunately sometimes they fail,” Kutcher tweets
She appeared to allude to the allegations in a statement in which she said that "there are certain values and vows that I hold sacred."
Also read: Demi Moore (@MrsKutcher) Needs to Change Her Twitter Handle
"It is with great sadness and a heavy heart that I have decided to end my six-year marriage to Ashton," she said in the statement. "As a woman, a mother and a wife there are certain values and vows that I hold sacred, and it is in this spirit that I have chosen to move forward with my life. This is a trying time for me and my family, and so I would ask for the same compassion and privacy that you would give to anyone going through a similar situation."
Also read: Demi and Ashton: A Marriage in Photos
Kutcher tweeted on Thursday: "I will forever cherish the time I spent with Demi. Marriage is one of the most difficult things in the world and unfortunately sometimes they fail. Love and Light, AK."
Moore, 49, and Kutcher, 33, married September 2005. Their marriage raised eyebrows for the 16-year-age gap between them, with many celebrity watchers appreciating the gender reversal of the frequent older man-younger woman pairings in Hollywood. It was the first marriage for Kutcher and the third for Moore, who was previously married to Bruce Willis. Moore and Kutcher have no children together.
Moore is the star of several blockbusters, including "Ghost" and "Indecent Proposal." Kutcher, a former star of "That '70s Show," recently returned to television to replace Charlie Sheen on "Two and a Half Men."
Rampant tabloid speculation about their marriage came to a boil last month when a 22-year-old San Diego woman, Sara Leal, described what she said was a September sexual encounter with Kutcher in an Us Weekly story headlined, "How Ashton Kutcher Seduced Me." She described in vivid detail a night of partying that led to nude hot tubbing and unprotected sex.
Kutcher, a fervent Tweeter who was one of the first celebrities to recognize and fully exploit the medium, has taken to it frequently to try to dispel the speculation. In late September, he tweeting a link to the music service Spotify to indicate that he was listening to Public Enemy's "Don't Believe the Hype." He later wrote, "When you ASSUMME to know that which you know nothing of you make an ASS out of U and ME."
At about the same time, Moore posted a photo of herself with her eyes closed and the caption, "I see through you…."