Adam and Lauren Silverman
Aaron St Clair/Splash News Online
08/01/2013 at 03:00 PM EDT
It doesn't look like Lauren Silverman's impending divorce is getting her down.
Despite her estranged husband Andrew Silverman listing "adultery" as reason for their split
, Lauren, 36 – who got pregnant
with Simon Cowell
's child while she was still married – stepped out all smiles on Thursday in the Hamptons.
There's a reason for the New Yorker's jolly appearance. A source told PEOPLE
that she "is ecstatic to be with Simon" and was unhappy in her previous relationship.
Revealing her barely-there baby bump when she was photographed out with her 7-year-old son Adam, Lauren was dressed casually in mid-length black leggings and a flowy white top.