  Interferometric signals are degraded by decoherence, which encompasses
dephasing, mixing and any distinguishing which-path information. These three
paradigmatic processes are fundamentally different, but, for coherent,
single-photon and $N00N$-states, they degrade interferometric visibility in the
very same way, which impedes the diagnosis of the cause for reduced visibility
in a single experiment. We introduce a versatile formalism for many-boson
interferometry based on double-sided Feynman diagrams, which we apply to a
protocol for differential decoherence diagnosis: Twin-Fock states |N,N> with $N
\ge 2$ reveal to which extent decoherence is due to path distinguishability or
to mixing, while double-Fock superpositions $|N:M> = (|N,M> + |M,N>)/\sqrt{2} $
with $N > M >0$ additionally witness the degree of dephasing. Hence,
double-Fock superposition interferometry permits the differential diagnosis of
decoherence processes in a single experiment, indispensable for the assessment
of interferometers.
