Few marriages have the potential to be as uneasy as that between an art museum and an art school. These relationships are beset with such existential questions as “To create — or to curate?” The partners are always mutually suspicious that the other is not contributing a fair share to household finances.

Behind the Corcoran Gallery of Art’s controversial decision Monday to consider moving out of its historic building at 17th Street NW, and maybe out of Washington altogether, is a bold gambit to thrive in a national cultural landscape where it has been much more common for museums and art schools to fall out of love and go their separate ways, say art educators and gallery officials.

Not all are convinced that pulling up stakes is the right move to stabilize the deficit-plagued gallery and affiliated Corcoran College of Art and Design, which share the same budget and board of directors but have somewhat different reasons for being.

“I just hope that this won’t impact the appeal of a Corcoran education,” said Kirk Pillow, a former provost at the Corcoran, who left in 2010 to become provost at the University of the Arts in Philadelphia. “We saw regularly that for students who would want to study at the Corcoran, a significant part of the appeal was studying in that building and having the opportunity to show their work through exhibits in that building.”

Bill Barrett, the Corcoran school’s dean in the early and mid-1980s, said he thought future generations of students wouldn’t care, as long as they remain closely tied to an excellent gallery collection.

“I think the Corcoran is genuinely looking for a way to do something really unique with these two arms of the institution, rather than let them drift apart,” said Barrett, who is executive director of the Association of Independent Colleges of Art and Design in San Francisco. “If they can do that, it would just be fabulous. It would be new and unique. And it may show others how to really use the assets of a collecting institution like a museum and the assets of a teaching institution.”

He added: “I think the big question, quite candidly, is, ‘Who’s going to want to buy that building?’ ”

The model of art schools attached to art museums emerged from 19th-century notions of how to teach art: Students learn by copying the works of masters. The only place to find masterworks was in museums. After World War II, as education became more regularized, with accreditation requirements, it got to be too much for many museums. They cut their schools or maintained little more than amateur art classes. By 1960, there were perhaps a dozen significant museum schools, from Portland, Ore., to Portland, Maine, Barrett said.

Now there are four: the Corcoran; the Art Institute of Chicago and the School of the Art Institute of Chicago; the Museum of Fine Arts Boston and the School of the Museum of Fine Arts Boston; and, in Philadelphia, the Pennsylvania Academy of the Fine Arts museum and school. (Some would also list the Rhode Island School of Design, although the school dominates its Museum of Art, Barrett said.)