The 69-year-old denies the allegations and has never been criminally charged.
Bikram yoga classes last 90 minutes in a humid room heated to 40C, and consist of 26 yoga poses formalised and popularised by Mr Choudhury in the 1970s.
From his California headquarters, he runs an empire of some 650 hot yoga studios worldwide, half of them in the US, and boasts celebrity devotees including Madonna, David Beckham, Jennifer Aniston and George Clooney.
Bikram yoga teachers must complete nine weeks of intensive training to be certified, and the most committed can pay US$12,500 (almost $17,000) to attend training courses taught by Mr Choudhury himself.
Roaming the heated room in nothing more than a pair of black Speedos, Mr Choudhury reportedly leads a punishing training regime that begins at 7am and stretches late into the night.
The lawsuits describe a charged atmosphere where the trainee teachers' diet, wardrobe, speech and even "the expressions on their faces" were supervised and constrained.
They were allegedly assured that Bikram yoga could cure cancer and increase its adherents' lifespans, and Mr Choudhury was a spiritual leader on a par with Jesus or Buddha.
In the most recent lawsuit, filed on February 13, Canadian former Bikram yoga instructor Jill Lawler claimed she was one of many students invited to massage Mr Choudhury during one of the mandatory late-night Bollywood movie marathons that were part of the training course.
Ms Lawler said Mr Choudhury groped her after she had massaged him "for hours" during such a screening in 2010, when she was 18.
He later reportedly apologised for his behaviour and vowed to "make her a champion".
Several weeks later, the lawsuit alleges, he raped her in his hotel room.
Ms Lawler said she wanted to leave the course after the initial incident, but having invested US$10,000 from her college fund to pay for Mr Choudhury's tuition, she felt obliged to continue.
She claimed the sexual assaults continued until 2013.
The public accusations against Mr Choudhury began to emerge that year, when another former student, Sarah Baughn, filed the first of the six lawsuits.
She claimed the yoga guru had made sexual advances during her training, and then assaulted her in a hotel room and later at his home.
In a statement, Mr Choudhury's lawyers strongly denied all the allegations against him.
"Their claims are false and dishonour Bikram yoga and the health and spiritual benefits it has brought to the lives of millions of practitioners throughout the world," the statement said.
"After a thorough investigation, the Los Angeles County district attorney declined to file any sexual assault charges against Mr Choudhury or the college for lack of evidence."
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- Independent
