Lauren Silverman Steps Out with Baby Bump and a Smile

Adam and Lauren Silverman

Aaron St Clair/Splash News Online

updated 08/01/2013 AT 3:00 PM ET

originally published 08/01/2013 AT 4:15 PM ET

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.

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