"I just find it. If it's there, if there's something scandalous lurking, I'll accidentally walk into it. I guess the relationship I've been in has been a particularly good soap opera."

"Everything just happened in the wrong order. I did my first proper film where I met Jude and we got together, and then the whole celebrity thing happened before I had any films out.

"I was probably perceived for a long time as someone who was just famous for...well, for a reason, but wasn't taken seriously as an actress," she told PEOPLE at the Sundance Film Festival. "People didn't want to pay attention to the fact that I actually took my work quite seriously.''

Miller, 25, began a romance with Law, 34, after appearing as on-screen lovers in Alfie. They got engaged in Dec. 2004 but Miller broke off the relationship after Law's affair with his children's nanny, Daisy Wright, was exposed the following year.

Miller has no regrets from the time she spent with Law.

"I loved working with Jude," she says of making Alfie. "He's an incredible actor. I actually liked that film, but maybe it was because I was falling in love and having a magical time making it."

Now, the actress has made a name for herself in films. On Monday Miller will be in New York City for the premiere of the Andy Warhol biopic Factory Girl, in which she stars as muse Edie Sedgwick reports PEOPLE.