  We elaborate on the functional integral describing the stochastic dynamics of
a spectator field during inflation, comparing its diagrammatic expansion to
that obtained directly from a perturbative solution of the corresponding
Langevin equation. We state Feynman rules for computing arbitrary temporal
$n$-point functions and perform some illustrative computations for a
$\lambda\phi^4$ interaction, paying attention to the role played by a
functional Jacobian determinant in the path integral. We also briefly consider
the case when the field contributes to the expansion rate, making the noise
multiplicative, which introduces additional vertices.
