Amber Heard and Elon Musk couldn't keep their hands off of each other during a romantic date in Sydney over the weekend

Amber Heard and Elon Musk just can’t keep their hands off of each other.

The love birds stepped out for a sweet date in Sydney, Australia, on Sunday, and looked to be in high spirits as they strolled arm-in-arm through the city.

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Heard, 31, wore a red dress with Musk’s suit jacket to keep warm. The stars were all smiles during their stroll, with both looking attentively at each other as they chatted.

Dating rumors began swirling last year when the actress and billionaire tech mogul were spotted out together several times amid their respective divorces — Heard’s contentious divorce from actor Johnny Depp was finalized in January and Musk filed for divorce from wife and Westworld actress Talulah Riley in January 2015.

“Elon and Amber are already very serious about each other,” a source told PEOPLE earlier this month. “She spends a lot of time at his house and is very comfortable there. Amber’s also gotten to know his kids and spends time with them as well.”

Although they began spending time together after Heard’s divorce, the Tesla founder first took interest in Heard in 2013 when he appeared in Robert Rodriguez’s film Machete Kills.

Image zoom Elon Musk/Instagram

“When the time was right and they were both single last year, he started pursuing her romantically,” a source previously told PEOPLE. “She was playing hard to get for a while, which made him even more interested.”

In April, Heard made the couple’s romance Instagram official with a photo of herself resting her arm against Musk, a kiss-mark clearly visible on his cheek.

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The actress and Musk were first seen together in Miami, where they were both staying at the Delano South Beach in July 2016.

“Elon is attracted to her edginess. She isn’t frightened about being different,” a source told PEOPLE of Musk. “She doesn’t get easily intimidated. She is very focused and loves to learn.”