The movie follows Diana's romance with London-based Pakistani surgeon Hasnat Khan, whom many friends of the princess say was her real love and the man she allegedly called "Mr Wonderful".
Based on Kate Snell's 2001 book "Diana: Her Last Love", the film suggests that Diana started dating Dodi Fayed to make Khan jealous -- a claim challenged by many close to the princess.
Diana and Fayed died when the Mercedes in which they were travelling slammed into a pillar in a Paris road tunnel in 1997 while being pursued by press photographers.
Ahead of the premiere in London's Leicester Square, Watts, a British-Australian actress who came to prominence in "Mulholland Drive" in 2001, admitted that she was taking a risk by accepting the role of the "People's Princess".
She was asked if she felt the film would offend Diana's sons.
"Hopefully if they get to see the film, they will feel that we have done it in a respectful and sensitive way," she told BBC TV.
But yesterday, Watts stormed out of a separate interview with BBC radio, apparently because a question offended her.
The surprised presenter, Simon Mayo, tweeted that Watts had "seemed a tad uncomfortable with the questions."
The film has been largely ignored by the royal family. Its producer Robert Bernstein claims the royals gave some help in allowing filming in Kensington Gardens, where Diana used to go jogging, although a spokesman for the royals told AFP the area was not under its jurisdiction.
Some critics have noted that Watts bears little physical resemblance to Diana, and had to wear a prosthetic nose for the film.
Watts claimed in an earlier interview that she "found herself constantly asking for (Diana's) permission to carry on" in the film.