  In the first part of the paper, we formulate several arithmetic transfer
conjectures, which are variants of the arithmetic fundamental lemma conjecture
in the presence of ramification. The ramification comes from the choice of
non-hyperspecial parahoric level structure. We prove a graph version of these
arithmetic transfer conjectures, by relating it to the quasi-canonical
arithmetic fundamental lemma, which we also establish. We relate some of the
arithmetic transfer conjectures to the arithmetic fundamental lemma conjecture
for the whole Hecke algebra in our recent paper arXiv:2305.14465. As a
consequence, we prove these conjectures in some simple cases. In the second
part of the paper, we elucidate the structure of an integral model of a certain
member of the almost selfdual Rapoport-Zink tower, thereby proving conjectures
of Kudla and the second author. This result allows us verify the hypotheses of
the graph version of the arithmetic transfer conjectures in a particular case.
