It's On! Gwyneth Paltrow and Brad Falchuk Take Their Relationship Public

Gwyneth Paltrow and Brad Falchuk Are Dating Publicly
Gwyneth Paltrow and Brad Falchuk
Jason Merritt/Getty; Kevin Winter/Getty

04/06/2015 AT 02:40 PM EDT

Gwyneth Paltrow is off the market again.

While her ex Chris Martin, 38, enjoyed a romantic weekend with actress Jennifer Lawrence, 24, Paltrow went public with her beau – television producer Brad Falchuk.

The Mortdecai actress, 42, made an appearance with the Glee producer, 44, at actor Robert Downey Jr.'s 50th birthday bash Saturday at the Barker Hangar in Santa Monica.

"Gwyneth and Brad have had a personal relationship for a long time,” a source tells PEOPLE. “It is still evolving."



The couple showed up to the star-studded soirée together, where they joined celebs including Jennifer Aniston, Justin Theroux and Jason Bateman.

Falchuk attempted to hop out of the car quickly to open Gwyneth's car door upon their arrival, but he didn't quite make it, according to a source.

"They laughed about it and seemed very happy to together," the source tells PEOPLE.

Following their party outing, the duo grabbed dinner Sunday evening in Santa Monica at Chinois On Main. The hostess greeted Paltrow with a big hug, an onlooker shared.

Paltrow has been linked to the American Horror Story co-creator for more than a year, but has flown under the radar with their relationship. They attended a pre-Oscars party together back in February, according to a fellow party goer.

In July 2014, the longtime friends vacationed together in Utah and were then spotted sharing a flirty meal at Vietnamese restaurant East Borough in Culver City, California, a source told PEOPLE in August.

"She seemed very comfortable with Brad," the source said.

Despite their new relationships, Paltrow and Martin have remained close ever since announcing their separation in March 2014 after 10 years of marriage.

"This is a natural evolution for Gwyneth and Chris as friends and as a couple," a source tells PEOPLE of the "private" pair.

"Between the two of them, there is no issue. They are good friends who respect one another deeply as parents," the source says.

Paltrow and the Coldplay musician also recently traveled together with their two children Apple, 10, and Moses – who turns 9 on Wednesday – on a family trip to Puerto Vallarta, Mexico.

RELATED VIDEO: Jennifer Lawrence And Chris Martin Spotted In Public For The First Time In Months

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