Not yet reviewed by Pith; the record is open.

We theoretically predict the giant and robust Josephson diode effect in quasi-one-dimensional topological Majorana nanowires in the regime with multiple subbands, which is expected to be relevant for the real experiment. In the multiband regime, the Majorana bound states and conventional Andreev bound states can naturally coexist, and respectively contribute to the fractional and conventional parts in the Josephson effect, with the former/latter having 4$\pi$/2$\pi$-periodicity. We show that the interplay between the two types of bound modes can produce a robust and giant diode effect in the deep topological phase regime. Notably, we unveil a novel spin parity exchange mechanism, occurring only in the multiband regime, which leads to a robust high efficiency plateau of the giant diode effect. This effect is a nontrivial consequence of the balanced Fermi moment shifts of the multiple subbands in tuning the external magnetic field. Our finding highlights the subband engineering as a powerful tool to optimize the Josephson diode effect realistically and provides a new feasible signature to identify topological phase regime in superconducting nanowires.