Mainly used refering as joining the fandom of a k-pop boyband, SEVENTEEN (CARATs). Seventeen has made and used this phrase since debut in their song "Shining Diamond" and their fans use this phrase all the time since it is special to CARATs. Seventeen refers their fans as "diamonds", hence slipping into the diamond life means joining the fandom (carats) / being a fan of Seventeen.
"Come on let's slip into the diamond life!" "Wow Seventeen's songs is so good I might slip into the diamond life."