  In this paper, we will consider scattering diagrams in the context of
infinite-derivative theories. First, we examine a finite-order
higher-derivative scalar field theory and find that we cannot eliminate the
external momentum divergences of scattering diagrams in the regime of large
external momenta. Then, we employ an infinite-derivative scalar toy model and
obtain that the external momentum dependence of scattering diagrams is
convergent as the external momenta become very large. In order to eliminate the
external momentum divergences, one has to dress the bare vertices of the
scattering diagrams by considering renormalised propagator and vertex loop
corrections to the bare vertices. Finally, we investigate scattering diagrams
in the context of a scalar toy model which is inspired by a
$\mathit{ghost-free}$ and $\mathit{singularity-free}$ infinite-derivative
theory of gravity, where we conclude that infinite derivatives can eliminate
the external momentum divergences of scattering diagrams and make the
scattering diagrams convergent in the ultraviolet.
