The Zero Dark Thirty actress vowed a "no actor" dating rule recently after scary experiences with relentless paparazzi - but has been won over by Hiddleston.
The Golden Globe-winning American star visited his family and friends this Christmas and it's thought the pair are "serious" about each other.
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35-year-old Jessica and Tom, 31, are keen to keep their love life out of the public arena.
She's said of dating famous men: "In this business it's very tough to maintain a relationship because we're like gypsies - always on the move.
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"And the more you share your relationship with the world the less special it becomes. So I always try to keep my dating life quiet."
On dating celebrities, she recently told InStyle UK: "I have dated an actor before, but since then, I've only been on a couple of dates with one and I was so freaked out someone was going to take a picture of us, because they were famous.
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"I realised I wanted just to be able to hang out with someone... And I didn't want to talk about the business, first of all.
"I love movies. But I love talking about them like when I was 15 years old. I'm a film fan, but I don't want to talk about auditions or what movie I'm gonna do. I find that so boring."
