  We develop a generalized field space geometry for higher-derivative scalar
field theories, expressing scattering amplitudes in terms of a covariant
geometry on the all-order jet bundle. The incorporation of spacetime and field
derivative coordinates solves complications due to higher-order derivatives
faced by existing approaches to field space geometry. We identify a jet bundle
analog to the field space metric that, besides field redefinitions, exhibits
invariance under total derivatives. The invariance consequently extends to its
amplitude contributions and the canonical covariant geometry.
