Movies may seem a more permanent medium than ephemeral art forms like theater and dance. But films are fragile things that often exist only fleetingly in their definitive state.

Take “The Leopard,” the opening-night film in To Save and Project, the Museum of Modern Art’s festival of recently restored films. It would seem that “The Leopard,” Luchino Visconti’s 1963 epic, has been in an almost continual restoration since it was first released, having been cut, dubbed and printed in an inferior color process during its commercial life. And yet the version in the festival represents a subtle but significant advance over even the superb Blu-ray edition issued by Criterion this year.

This latest version of “The Leopard” is among more than 35 films from around the world in this eighth edition of To Save and Project, which begins Friday night. Almost all the movies are being seen in New York for the first time in their refurbished form; several are being shown in the United States for the first time in complete or expanded versions. “The goal of preservation is to get a film back up on the screen,” said Joshua Siegel, an associate curator at the Modern who, with his colleagues Anne Morra and Katie Trainor, is one of the organizers of the series.

It’s bad enough, to cite a common estimate, that 90 percent of all American silent films and 50 percent of American sound films made before 1950 appear to have vanished forever. But even the films we have often live on in diminished states. An astonishing number of famous titles  like “King Kong” and “His Girl Friday”  no longer exist as original camera negatives, but survive only as degraded duplicates and damaged release prints.