Since he first came on the art scene in the 1980s, Schnabel has shown a great talent for attracting attention to himself - a poster boy for the "me generation," who likes to go out publicly in pajamas or a sarong.
As correspondent Morley Safer reports, you can't help but notice this man, even admire his belief in his own genius. Love him or hate him, you must admit he has an ego the size of Manhattan.
One of his large paintings, according to Schnabel, sells for around a million dollars.
Buy it or dismiss it, people have been arguing about Schnabel's art for 30 years. And it has paid for some spectacular real estate: one home in Montauk on Long Island, and a palazzo in New York's Greenwich Village.
The Greenwich Village palazzo - known as the pink palace - is his base of operations. Outside, there are 360 degrees of killer views. Inside, touring the place with him, you feel like Gulliver in the land of the giants, surrounded by huge sculptures, 20-foot high ceilings, and Schnabel paintings that are both larger than life and larger than some New York apartments.
The living room is dominated by one of his favorite works, a painting of a girl's head. It's one of a dozen similar big girls Schnabel has painted in recent years, all of them inspired by a small amateur painting he found in a junk shop years ago.
"My father said to me, 'How come you painted her eyes out?' And I said, 'So you look at her chin,'" Schnabel remembers.
What's it all about? As Schnabel well knows, explaining art can be an elusive and treacherous pursuit.
He's constantly on the prowl for new surfaces, painting on old tarpaulins, rugs, and velvet. His current passion is for a stash of old navigation charts that seem to say to him "color me purple."
"I probably paint like a jazz musician. I know where to begin, but I don't really have necessarily an idea of how the thing's going to turn out. And I'm sort of leaning toward a divine light. And I think maybe it'll hit me, maybe it won't. But in making a movie, it's the same thing," he told Safer.
Divine light or earthly savvy, there's no questioning his success as a filmmaker: his movies were nominated for five Oscars, and he himself won top prizes at the Golden Globes and the Cannes Film Festival.
"I thought I was too old to be a movie director. But once I was doing that, Dennis Hopper was on the set. He said, 'Looks like you've been doin' this for 40 years,'" Schnabel remembers.
There was "Basquiat," the tragic biography of the young artist who died of a toxic mix of drugs at age 28, a victim of the overheated New York art world of the 1980's, a culture Schnabel knew firsthand.
"Before Night Falls" was an uncompromising portrait of the persecuted Cuban novelist Reinaldo Arenas, who died of AIDS, believing that writing was the best revenge.
"The Diving Bell and the Butterfly" is a true and compelling story about a French man-about-town suddenly imprisoned by a rare and almost total paralysis.
Making the films, Schnabel quickly developed his own method for working with actors: short on rehearsal, long on improvisation. "My technique is, you throw everybody in a hole and if they can climb out, you go home at the end of the day - and that includes me," he explains.
What if they don't "climb" out?
"If they don't, then the movie dies," Schnabel tells Safer.