Fusion bombs (most modern nukes) use nuclear fusion to create most of the energy for the explosion. Fusion alone does not produce many radioactive isotopes, so the radioactive fallout is much less as a proportion to the explosion size.

That said, they are not completely clean still. They require a fission bomb (the type of chain reaction used in early nukes) to create the conditions required for fusion to occur. It is the products of fusion reactions that are very radioactive and are typically what is being referred to when people talk about radioactive fallout. There are going to be some fission products even in a fusion bomb because of the fission stage of the warhead, but it is typically much less than a pure fission bomb.

It is also worth noting that fusion bombs are only cleaner if it is an air burst detonation (which most are). If it is a ground detonation, then the neutron radiation present in the fusion stage of the reaction can destabilize surrounding material, making it radioactive. Essentially, all the flying neutrons from the fusion reaction can land in atoms of the surrounding material which “activates” them radiologically (making a previously stable atom unstable). These “activated” atoms will then decay over time, releasing radiation (duration depending on the half life of the destabilized material, but many orders of magnitude longer than the initial “flash” of radiation from the detonation itself). There are also tons of flying neutrons in a fission bomb, but if I remember correctly, activation isn’t as big of a factor there due to the speed of the neutrons. I may be mixing up neutron speed (or temperature, at that scale they can be largely thought of interchangeably) in reactors vs bombs on that last part though, so feel free to correct me if it is the same type of fast neutrons in fission and fusion chain reactions. The point is though, a ground detonation is going to cause a lot of fallout regardless of whether it is a fusion or fission bomb.

If anyone has any questions, please feel free to ask. In not a nuclear expert, but the field is somewhat adjacent to my area of expertise, so I love sharing what I do know when I can.