Dave Quinn
January 16, 2018 08:31 AM

Days after their Malibu dinner date, Chris Martin and Dakota Johnson were seen hitting the beach — walking arm in arm on the sand as they took in the California sun.

The pair, who have been fueling romance rumors for months, seemed as close as can be for their Sunday stroll. The Fifty Shades of Grey actress, 28, wore a floral printed coverup while the Coldplay frontman, 40, wore black shorts, a grey athletic top and a baseball cap.

A source tells PEOPLE Martin and Johnson spent “most of the weekend together in Malibu.”

“They seem to be getting more serious,” adds the source. “On Friday, they had dinner with friends. They also hung out at Chris’ house and went for a beach walk. They didn’t see each other over the holidays and seem excited to be catching up now.”

Just last week, Martin and Johnson were seen grabbing food and drinks at Soho House in Malibu, California, where they were snapped with big grins on their faces. An eyewitness told PEOPLE, “Chris and Dakota arrived together in Chris’ car. They met up with friends and had a fun night. They both seemed very happy. They were flirty, and also left the restaurant together.”

Dakota Johnson and Chris Martin
DOBN/RMBI/BACKGRID

Johnson and Martin first sparked gossip of a blossoming relationship after being spotted on a mid-October sushi date in Los Angeles. They were “cozy, laughing and affectionate,” said a source at the time.

The following month, Johnson was photographed by fans hanging out in the sound booth at Coldplay’s concert in Argentina.

Chris Martin and Dakota Johnson
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RELATED VIDEO: Gwyneth Paltrow, Ex Chris Martin and Her Rumored Fiancé Brad Falchuk Grab ‘Sunday Brunch’ Together

Martin was married for 10 years to Gwyneth Paltrow before the pair split in March of 2014. The two share children, Apple, 13, and Moses, 11.

Johnson previously dated model/rocker Matthew Hitt.

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