Display an image or UIImage with a plain CALayer

I've often read that using a CALayer rather than a UIImageView is an performance boost when it comes to heavy image usage. That makes sense, because UIImageView causes 3 copies of the image in memory, which is needed for Core Animation. But in my case I don't use Core Animation.

How can I assign a UIImage (or its image data) to a CALayer and then display it?