Elizabeth Vargas' husband Marc Cohn has spoken out about the recent rumors that say he cheated. Cohn, a folk-rock singer known for hit song "Walking in Memphis," spoke to People about the scandal, but did not give a definite answer. Rumors began earlier this week that the singer had been unfaithful to wife and ABC 20/20 anchor Elizabeth Vargas while she was in rehab. "I will not comment on what is an extremely sensitive and private family matter," Cohn said. "Addiction and recovery are serious challenges and it's been a tough road for all of us." "I have been supportive of Elizabeth in the past -- and will continue to be -- regardless of the long-standing issues in our relationship," he continued. Vargas checked into rehab late last year after she admitted she was an alcoholic, and has since returned to television. The New York Post was the first to report on Wednesday that Cohn had an affair with mutual friend and Flywheel co-founder Ruth Zukerman while Vargas was away. Vargas and Cohn were married in July 2002. The couple have two children together, and two from Cohn's first marriage.