On June 16, 1961, the Soviet ballet star Rudolf Nureyev slipped away from his KGB minders while on tour in Paris, and within a week, he was doing his jetés and echappés in The Sleeping Beauty with a French company. Ten years later, 13,000 Jewish refugees left the Soviet Union; over the next three decades, the U.S. accepted hundreds of thousands. In 1979, when Bolshoi dancers Valentina Kozlova and Leonid Kozlov ducked out the garage door of the Shrine Auditorium in Los Angeles, the U.S. granted them asylum the next day.

Today it's not ballerinas and Jews fleeing Russia in droves, but a new group of Putin-era refuseniks: LGBT people. Facing a discriminatory new law against "propaganda of non-traditional sexual relations" and a spike in homophobic violence, many see getting out of Russia as a matter of life and death.

Slava Revin, a 31-year-old activist who arrived in the U.S. in July, is part of a fast-growing community of young LGBT Russians who've flocked to New York, Washington, D.C., and other U.S. cities. Like the Soviet Jews and dissidents who fled decades before them, Revin and his peers have formed a tight network, helping one another adjust to life in America and advocating for the rights of those left behind.

"I can't just come here and keep my mouth shut," said Revin, who has spoken about threats against Russian LGBT people in a video for Freedom House and called on Philadelphia Mayor Michael Nutter to terminate the sister-city relationship with his hometown, Nizhny Novgorod.

Revin sat down with BuzzFeed a few months ago in Washington's historically LGBT-friendly Dupont Circle. Not long after he escaped Russia, where gay bars often operate underground, he found himself living down the block from Larry's Lounge, a neighborhood spot with an outdoor patio and a neon rainbow sign.

In June, after someone he believes is a police officer threatened him online, Revin filled a suitcase with documents — records of his LGBT rights activism and work supporting HIV-positive men, copies of letters he'd written to local officials, his passport, his birth certificate — and some clothes. He called his parents and told them he was going away for a while. Then he took a train to Moscow.

Revin had made plenty of trips to the Russian capital in the course of his activist work, but this time he knew he wasn't going back to Nizhny Novgorod. He spent the night at a friend's apartment, the first in a months-long string of temporary homes. A few weeks later, with a tourist visa and an invitation to attend a conference in the U.S., he boarded a flight to JFK Airport. After he arrived, he emailed Immigration Equality, an organization that assists LGBT asylum seekers from around the world. He needed a lawyer and a place to stay.

Revin's message joined a deluge of inquiries from other LGBT Russians looking to settle in the U.S. Immigration Equality says calls and e-mails about asylum shot up after the "propaganda" ban passed last summer. In 2013, the organization opened 28 new Russian asylum cases, an all-time high compared to the previous average of 11 per year. In January, the group hired a Russian-speaking staff member to help deal with the influx. Immigration Equality currently has 44 Russian cases open and has won asylum for eight LGBT Russians since August.

Citing a long waiting list for legal help, and hoping it would be easier to find housing outside New York, Revin moved to D.C. There he secured a room and pro bono counsel through the Center Global, a program of The DC Center for the LGBT Community. In a statement, Immigration Equality Legal Director Aaron Morris said the organization is almost always able to secure representation for its clients, though it can take a few weeks.

Revin also sought contacts and advice from the Russian-Speaking American LGBT Association, the only organization in New York that focuses on supporting the Russian-speaking LGBT community. Yelena Goltsman, the group's founder and co-president, said she receives three or four emails a week from LGBT people who are thinking about leaving Russia. She sees it as a sign anti-LGBT sentiment is intensifying.

"People don't just get up and leave their country," she said. "LGBT people are basically [the] new Jews."

Revin uses the same metaphor. With the media spotlight of the Sochi Olympics gone, he anticipates further crackdowns. "You can compare it to Germany in 1939 when everyone forgot about the Jews," he wrote in an email to BuzzFeed after the Games. "They will intimidate people, beat them, activists will be arrested. It's a matter of months."

Goltsman, 51, lives the life many Russian-speaking asylum seekers hope to find in America. She was married to a man when she emigrated in 1989 from Ukraine, then part of the Soviet Union, where homosexuality and religion were banned and state-sponsored anti-Semitism was pervasive. In the U.S. she was able to openly express her Jewish identity, as well as her sexual orientation, and eventually came out to her family.

Goltsman fell in love with a woman she met at Congregation Beit Simchat Torah, a West Village synagogue led by a lesbian rabbi. In 2011, her adult children joined her under a chuppah as she married Barbara Freedman before 120 guests. The Jewish ceremony took place at a refurbished brass foundry in Brooklyn, and the reception featured a massive amount of Russian food. The couple legally became spouses under New York State's Marriage Equality Act.

Goltsman, who calls her personal journey a miracle, points out that she left the USSR with relatives and knew she could count on Jewish organizations in America for support. She's trying to build a similar community for today's LGBT asylum seekers, many of whom are single young men navigating the transition largely on their own.

When Revin arrived in America, he knew he would need a lot of help to start over. He didn't understand much English and had limited cash, but for the first time in weeks, he felt safe. "You run and run and run for a long time," he said of the decision to seek asylum in the U.S. "You're winded, but you breathe and you understand you don't have to run anymore."