A Japanese woodcut from 1734
really knows. The whole subject of the origin and early
history of origami is a difficult one. There is simply
not enough information to be sure of anything and often
the best we can do is guess.
One theory is that, since folding paper is such a natural thing to do, it is possible - indeed quite likely - that some basic kind of origami began in China soon after paper was first invented. On this theory the idea then spread from China to Korea and from Korea to Japan. There is no proof of this theory, but since this is what happened with papermaking, writing and many other aspects of oriental culture it is perhaps quite likely that it happened with origami as well.
An extension of this theory is that origami then spread to the West through contact with the Orient, particularly with China. This is certainly what happened with papermaking. On this theory the similarity of designs in various traditions is evidence of cultural cross-fertilisation.
On the other hand, since folding paper is such a natural thing to do, it is equally possible - indeed, quite likely - that origami began quite independently in many different countries - China, Japan, Germany and Spain, for instance - at many different dates. On this theory the similarity of designs in various traditions need amount to no more than the well documented fact that identical simple origami designs are quite often discovered by different paperfolders in diverse places at diverse times.
At present there is insufficient evidence to choose between these competing theories, though the likelihood is that both are true in part. There was some independant origination and some cross-fertilisation. What is certain, however, is that the Japanese paperfolding tradition developed further and became more diverse than the tradition of any other country and that it was in Japan that the mundane act of folding paper first developed into a true decorative craft.