TITLE: Are any two K3 surfaces over C diffeomorphic?
QUESTION [5 upvotes]: Let $S$ be a K3 surface over $\mathbb{C}$, that is, $S$ is a simply connected compact smooth complex surface whose canonical bundle is trivial. I recall reading somewhere that any two such surfaces are diffeomorphic, however I can't for the life of me remember where, or how the proof goes. 
Does anybody know a good reference to a proof, or can provide a proof?
Thanks,
Dan

REPLY [6 votes]: I find this reference quite readable:
Le Potier: "Simple connexité des surfaces K3", in Asterisque 126, 1985.
I haven't read Kodaira's paper (in Joel's answer), so I don't know whether it is the same argument, but Le Potier also deforms to quartic surfaces.