  In this paper, we consider the problem of reconstructing trees from traces in
the tree edit distance model. Previous work by Davies et al. (2019) analyzed
special cases of reconstructing labeled trees. In this work, we significantly
expand our understanding of this problem by giving general results in the case
of arbitrary trees. Namely, we give: a reduction from the tree trace
reconstruction problem to the more classical string reconstruction problem when
the tree topology is known, a lower bound for learning arbitrary tree
topologies, and a general algorithm for learning the topology of any tree using
techniques of Nazarov and Peres (2017). We conclude by discussing why arbitrary
trees require exponentially many samples under the left propagation model.
