After dropping out of his country's National Film School, he scored a surprise hit at the Danish box office in 1996 with his debut "Pusher", a low-budget drama about Copenhagen's drug scene.
The film also launched the career of Danish actor Mads Mikkelsen, who rose to global fame as the Bond baddie Le Chiffre in "Casino Royale".
Mikkelsen's place on this year's Cannes jury may have put Refn and his film about cannibalism on the Los Angeles fashion scene in a difficult spot.
Refn once said that when he and Mikkelsen work together "it's like we're united as one person".
However, it's a purely work-based relationship. "We do not see each other if we're not working," Mikkelsen said in a 2012 documentary.
"I mean he can only, and I say only, talk about films. And I can almost only talk about sports," he added.
With his thick-framed glasses and hipster cardigans, there is little about the soft-spoken Refn to suggest he is a self-confessed "pornographer" of violence.
"We humans are physically created to exert violence. Since we are forced to repress our violent tendencies, we get a need to see images of violence," he once told a Swedish newspaper.
Viewed by many as Denmark's first real gangster movie, "Pusher" showed the violent underbelly of the country's picturesque capital: the central Vesterbro district's flourishing drug trade and those who control it.
Filmed with a handheld camera in chronological order, Mikkelsen has claimed it inspired Danish directors Lars von Trier and Thomas Vinterberg who founded the avant-garde filmmaking movement Dogme 95 -- "even though they will never admit it," he said.
While promoting 'The Neon Demon' on Friday, Refn had some choice awards for von Trier.
"Lars is Lars. He's done a lot of drugs," Refn said.
“The last time I saw Lars he asked my wife if she wanted to have sex. He found some other slut," Refn said, adding that von Trier is "over the hill".
The Neon Demon trailer - story continues below
From flop to 'Drive'
Refn's position at this year's Cannes festival is a far cry from where he stood after writing and directing his first English-language film, "Fear X".
His first attempt to make it in Hollywood flopped so badly it pushed him into bankruptcy and forced him to return to Denmark, where he made two "Pusher" sequels and even directed a "Miss Marple" episode to make ends meet.
The "massive failure" of his first international production "still haunts me to this day" but knocked "some sense into me", he said later.
It wasn't until 2008 that he ventured overseas again, with "Bronson", which tells the story of one of Britain's most notorious criminals, Charles Bronson.
He finally cracked Hollywood in 2011 with "Drive", starring heartthrob Ryan Gosling as a stuntman who moonlights as a getaway car driver, earning him the best director award at that year's Cannes festival.
"We're very similar in many ways," he said of the actor in a 2013 interview with Britain's The Guardian. "We're both mama's boys. We both worship women as goddesses."
Their second collaboration in 2013 fared less well. Blood-spattered revenge tale "Only God Forgives" was booed at a press screening in Cannes and left many in the auditorium wincing or unable to watch.
In one scene, Thai actor Vithaya Pansringarm -- playing an ex-cop on a mission to purge Bangkok of sleaze -- pins a man to an armchair with knives and stabs him through the eye.
"The movie is so devoid of emotion that its ritualised gore acts as a narcotic," The New York Times wrote in a review.
"Three words should suffice: pretentious macho nonsense," it added.
Online giant Amazon has acquired the distribution rights to "The Neon Demon" and will release it in US cinemas as well as on its video streaming service.
"The day that television was invented, cinema changed," Refn told the Deadline Hollywood website in February.
"Now it's a screen in (a) stadium Imax, but it's also an iPhone and both are equally as important," he added.