Though Peruggia claims he did it out of patriotism, I've always nursed the theory that, during its absence, the original was used as reference to create several extremely good fake versions. These could be sold as the original, since everyone knew it had been stolen, and each would think they had the real one. Then the original is returned, and the buyers are without recourse. What are you going to do, tell the police? And of course Peruggia et al would say nothing.

I suspect this isn't true, but the fun part is that it could be and no one would ever know. So I'm choosing to believe it is so.