  We study the soft limit of a recently proposed generalization of the
biadjoint scalar amplitudes $m^{(k)}_{n}$, which have been conjectured to have
a relation to the tropical Grassmannian $\text{Tr G}(k,n)$. Using the CHY
formulation along with the Global Residue Theorem, we prove the soft
factorization for $m^{(k)}_{n}$ amplitudes for arbitrary $k$ and $n$. We find
that the soft factors are in direct correspondence to vertices of the
associahedron $\mathcal{A}_{k-1}$, and hence take the form of $m^{(2)}_{n}$
amplitudes. This entails that all scattering amplitudes of the ordinary
biadjoint scalar theory can be interpreted as an infinite family of soft
factors. Additionally, Grassmannian duality reveals that generalized amplitudes
$m^{(k)}_{n}$ with $k>2$ satisfy not only a soft theorem, but also a
non-trivial "hard" theorem. We perform numerical checks of our theorems against
previous results for $\text{Tr G}(4,7)$ and $\text{Tr G}(5,8)$, thereby
providing strong evidence of their relation with the CHY formulation.
