Amy Winehouse and husband Blake Fielder-Civil have returned to the UK after a brief holiday abroad.
The Sun reports the singer as saying that they would recover from their problems soon, as the pair walked through Gatwick airport carrying a framed photograph of their wedding day.
Speaking about why he was carrying the picture in public, Fielder-Civil said: "I like having it with me. It’s beautiful. It reminds us of what we have together."
He also denied taking drugs saying that reports of the couple's substance abuse problems were mere "speculation".
"We vehemently deny the stuff about drugs. It’s speculation, it’s rubbish.
"We admit things have been a little crazy and have to change. We’re going to sort ourselves out," he added.
Winehouse also spoke to the newspaper, defiantly saying that the couple would not end up like Sid Vicious and Nancy Spungen. Sex Pistol member Vicious was arrested over his girlfriend's death in 1978 and died a year later after overdosing on drugs.
The Rehab singer told the paper: "We are not going to end up like them. We’re in love and have everything to live for."
The star is expected to attend the Mercury music prize ceremony today, where her album Back to Black has been nominated for an award.
Last week, Winehouse was forced to cancel tour dates in the US amid claims of reported drug abuse.
The soulful star also pulled out of a planned performance at the MTV video music awards after both her and her husband were reported to have checked into drug rehabilitation centres.
Her record company Universal Records said the cancellation was part of a "continued effort to support Amy Winehouse's wellbeing".
The singer has hardly been out of the headlines in recent weeks, with newspapers chronicling her life with her partner.
Both are believed to have visited drug rehabilitation centres and Winehouse was pictured covered in bruises and with blood on her shoes after an apparent falling-out with her partner.
Earlier this week, Winehouse's in-laws spoke out about what they consider to be the couple's drug addiction and urged the singer's fans not to buy any more of her records.