Carlos Alvarez, Getty Images / Jeff Vespa, FilmMagic

Robert Pattinson and Dylan Penn really dig one another, but they're both pretty scared of settling down together. Is their fling over as soon as it began?

The 'Twilight' actor, 27, and the model daughter of Sean Penn and Robin Wright, 22, only just began dating, but they're already getting nervous about the speculation around their budding relationship.

"She doesn't want to be known as Rob's girlfriend," a source dished about Penn to Us Weekly. "She's afraid to get serious with him and lose her privacy."

Considering all the craziness surrounding Pattinson and his ex, Kristen Stewart -- especially after she publicly cuckolded him with her married director -- we don't blame her. Still, don't think R-Pattz is in any rush to nail down a commitment, either.

"Rob isn't ready to be exclusive with anyone right now," another source added. "He's just enjoying himself."