Hyperdiffusionism is the idea that when different cultures share particular elements, one culture must have adapted it from the other. For a hyperdiffusionist, it would be unlikely that the same invention or innovation could arise in different places; this is a stronger position than straight-up diffusionism, which just stresses that human societies tend to steal a lot of good ideas from their neighbors.
In the mid-twentieth century, hyperdiffusionism was somewhat popular amongst anthropologists but it enjoys little support nowadays. Historians, anthropologists and archaeologists now argue that since human minds tend to work in a similar manner regardless of context, many discoveries (writing, agriculture, the number zero) or cultural practices (building pyramids, worshiping the Sun, ball games) probably developed independently in various parts of the world.
Anyway, Hyperdiffusionism doesn't explain why such popular vegetables as tomatoes, corn, potatoes and capsicum could still be exclusive of the New World until 1500 A.D.
Hyperdiffusionists will cite peoples such as the Egyptians, the Sumerians, the Mayans or the ancient Chinese as foundational to "human civilization," but nationalists all around the world have often argued that their culture was the one to figure out all the important stuff first. Some particularly whacky people might even ascribe human civilization to made-up places like Atlantis, Mu or Lemuria or claim it comes from outer space.
Perhaps the most famous proponent of hyperdifussionism was the Norwegian adventurer Thor Heyerdahl. Heyerdahl sailed from Peru to Easter Island on an Inca-style raft to prove Polynesia was settled from South America and crossed the Atlantic on an Egyptian-style raft to prove the Egyptian origins of various pre-Columbian civilizations. Other notable hyperdiffusionists were Grafton Elliot Smith and William James Perry.
Hyperdiffusionism has the nasty trait of being an easy way to justify belittling non-Western cultures or rob them of their history. A notorious example is Greater Zimbabwe, an urban center built by an indigenous Bantu kingdom around the eleventh century but which for centuries had been considered a Roman or Phoenician colony by European archeologists. Also many pre-Columbian trans-Atlantic contact theories tend to be of the 'Mayans were too stupid to have built that, so it must have been Egyptians/Chinese/extraterrestrials' kind.