  Massless particles in $n+1$ dimensions lead to massive particles in $n$
dimensions on Kaluza-Klein reduction. In string theory, wrapped branes lead to
multiplets of massive particles in $n$ dimensions, in representations of a
duality group $G$. By encoding the masses of these particles in auxiliary
worldline scalars, also transforming under $G$, we write an action which
resembles that for a massless particle on an extended spacetime. We associate
this extended spacetime with that appearing in double field theory and
exceptional field theory, and formulate a version of the action which is
invariant under the generalised diffeomorphism symmetry of these theories. This
provides a higher-dimensional perspective on the origin of mass and tension in
string theory and M-theory. Finally, we consider the reduction of exceptional
field theory on a twisted torus, which is known to give the massive IIA theory
of Romans. In this case, our particle action leads naturally to the action for
a D0 brane in massive IIA. Here an extra vector field is present on the
worldline, whose origin in exceptional field theory is a vector field
introduced to ensure invariance under generalised diffeomorphisms.
