11/17/2011 AT 4:30 PM ET
“It is with great sadness and a heavy heart that I have decided to end my six-year marriage to Ashton,” says Moore in a 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.”
She adds: “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.”
Kutcher Chimed: “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.”
The split follows reports that 22-year-old Sara Leal alleged a one-night stand with Kutcher on his sixth wedding anniversary with Moore in September.
In the weeks since, Moore, 49, and Kutcher, 33, appeared to be working on their relationship, showing up together for Yom Kippur services and were spotted building a campfire at a lake near Santa Barbara, Calif., alongside their Kabbalah instructor.
The two stars weathered a previous cheating scandal one year earlier, when Brittney Jones, 22, claimed she had sex with Kutcher in July 2010. At the time, they took a trip to Israel for what the actor described as a spiritual journey.
Those who know the couple say the union had been under strain for some time, and spending more time apart.
“Demi loves Ashton as much as she hates public humiliation,” a source close to the couple told PEOPLE when Leal’s allegations first surfaced. “The marriage isn’t good right now.”