It is not diffusion but rather active transport.Just to make it simple , certain proteins called "export proteins" or ' exportins ' bind to the mRNA (which carries nuclear export signals ) within the nucleus.The exportin protein is also bound to Ran-GTP (compare to ATP for simplicity) .The exportin carries the mRNA to the cytoplasm where Ran-GTP disassociates in to Ran-GDP and mRNA is let free from the exportin protein.