Florence Pugh will skip Monday's press conference for Don't Worry Darling at the Venice International Film Festival

although she still plans to walk the red carpet for the premiere later that day, according to Variety.

A source close to the Dune: Part Two production tells PEOPLE that Pugh is flying into Venice from set 

Her absence from the event comes amid speculation that Pugh is on bad terms with Don't Worry Darling costar and director Olivia Wilde,

Another source adds that this had always been the plan, though it just came to light with the Variety report.

Regarding rumors of a pay disparity between the Academy Award nominee, 26, 

her co-lead Harry Styles, Wilde, 38, said: "There has been a lot out there that I largely don't pay attention to.

But the absurdity of invented clickbait and subsequent reaction regarding a nonexistent pay disparity between our lead

"I'm a woman who has been in this business for over 20 years, 

it's something that I have fought for myself and others, especially being a director.