But in rare moment of openness, Depp gushed about Heard when I chatted with him at the L.A. premiere of The Danish Girl.
"We connect on a lot of levels but the first things that really got me was she's an aficionado of the blues," the Black Mass star said. "I would play a song, some old obscure blues song, and she knew what it was."
He continued, "She's very very literate. She's a voracious reader as I have been, so we connected on that as well and she's kind of brilliant and beautiful."
"I'm a lucky man," Depp said with a smile.
He also praised her work in The Danish Girl. The movie, adapted from David Ebershoff's book of the same name, tells the story of Lile Elbe (Eddie Redmayne), the first transgender woman to undergo sexual reassignment surgery in the late 1920s in Germany with the support of her wife, fellow artist Gerda Wegener (Alicia Vikander). Heard plays a dancer friend of the couple's.
"It's a very beautiful movie and I'm very proud of her," Depp said. "She worked very hard."
He also said he thought Heard was a "perfect" fit for the period drama. "It looks like where she belongs," Depp said. "I always felt like I was supposed to be in a different time and I kind of felt that way about her the first time I saw her, so it looks right and perfect for her."
The Danish Girl is in theaters on Nov. 27.