“I just loved his face, his voice, his approach to acting, and thought he would be ideal,” Mr. Jarmusch said. “He likes to figure out how the character moves and then just go with that without thinking too much.”

Then there was the not insignificant fact that Mr. Driver was a former Marine from small-town Indiana who attended Juilliard, and Mr. Jarmusch’s film was about a working-class guy who’s an artist.

“And I thought, well that’s an interesting combination,” Mr. Jarmusch said.

Mr. Driver also drew the admiration of Martin Scorsese, who beckoned him to discuss the role of Father Garupe, a 17th-century Jesuit priest on a mission from Portugal to Japan in “Silence,” his passion project, now in theaters.

“I love the way he moves, his sense of himself on camera,” Mr. Scorsese wrote in an email. “For the role of Garupe, we needed someone who could look like they lived in the period — something that just isn’t true of all that many actors. Adam could have stepped out of a Dutch or Flemish or Italian painting. And he also has that remarkable baritone voice. He’s talented, of course, and very, very brave.”

That bravery included starving off 51 of his 206 pounds while enduring arduous shoots in the steamy, rain-pummeled hills of Taiwan, or submitting to repeated submersions in the frigid sea.

“Of course, we all understood that it was very important that they had to actually be thin and hungry,” Mr. Scorsese wrote. “There was no faking it. They worked with a nutritionist, but it was very hard on them.”