Cibrian, 40, addressed the rumours during a press junket of his upcoming film 'The Best Man Holiday', reported Us magazine quoting Entertainment Tonight.
"(The divorce, affair rumors have) been going on for so long. They're just absurd, and to give any validity to any of these things, it's crazy," Cibrian said.
The actor and 31-year-old Rimes married in 2011 following an affair that made them one of the most controversial couples in Hollywood.
Rimes and Cibrian had an extramarital affair while shooting 'Northern Lights'. They subsequently went public with their relationship and divorced their significant others.
Cibrian insists that his marriage is going well.
"We have such a great marriage -- very functional.