But now the mystery has been solved.
Walsh, 39, is dating Alex Young, a production co-president at 20th Century Fox, with a string of big-time credits to his name, including X-Men: The Last Stand and Fantastic Four.
"He's a hotshot," says a friend. "But Alex also has substance. He's a good guy."
Walsh, who stepped out with Young at an April 28 fund-raiser for Barack Obama in Los Angeles, has become pretty hot herself.
On Thursday, she starred in a two-hour special episode of Grey's Anatomy, "The Other Side of This Life," which featured her character, Dr. Addison Montgomery, contemplating a move to another hospital.
And Walsh, who was most recently romantically linked to Brothers & Sisters star Dave Annable, recently told Best Life magazine she's a late-bloomer in love, but is finally ready for a serious relationship.
"I don't need someone with a hot body," she said.
"He can be fat or overweight and have a belly. It's very much about style and substance and humor, interest, curiosity and really being smart."