According to Sophia's mother Samantha Burke, their one-month-old daughter looks just like the 36-year-old actor and has already perfected his sultry expression.
She said: "Her features are more like Jude's. She has his chin and nose, and she does a little pout that I notice that he's done before. I think her eyes are more like mine, though. You can't always tell when they're so young but they don't seem to have that big, glassy look that his do - mine are a little smaller and more like hers. Luckily both her parents have good eyes."
The 25-year-old model fell pregnant during a fling with Jude - who already has three children Rafferty, 14, Iris, eight, and Rudy, seven with his ex-wife Sadie Frost - earlier this year after they met at a nightclub.
Samantha explained: "I instantly knew who he was, but he seemed really funny - he was cracking jokes with people and he included me in that. The next thing I knew I was on the pavement outside, being twirled around - it was a lot of fun. Following that initial meeting, Jude and I went out several times. He was a lot of fun to be around, always making me laugh.
"He's a great actor, and very good looking - you could say I was a fan. He was funny and very down to earth, which I would have expected - it was like a breath of fresh air.
"I knew that as we headed in separate directions our relationship would not continue. And I was OK with that. I was living in the moment and I really enjoyed all my time with Jude. I have no regrets."
Although Samantha is yet to introduce her daughter - born on September 22 - to Jude, she is convinced he will be a good parent.
She said: "He's a great father to his three kids. She's his daughter, and I believe he'll come through. I mean, once you see her face, how can you deny it?
"It would be great if we can have a friendship and be cordial.
"Hopefully, he'll be a big part of her life and she'll be proud of him as her father."
The full interview appears in Britain's Hello! magazine on sale now.
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