The regularity of difference divisors

For a prime number $p>2$, we explain the construction of the difference divisors on the unitary Rapoport-Zink spaces of hyperspecial level and the GSpin Rapoport-Zink spaces of hyperspecial level associated to a minuscule cocharacter $\mu$ and a basic element $b$. We prove the regularity of the difference divisors, find the formally smooth locus of both the special cycles and the difference divisors, by a purely deformation-theoretic approach.