We present photoionization modeling of galaxy populations at z ∼ 0, 2, and >6 to bridge optical and far-infrared (FIR) emission-line diagrams. We collect galaxies with measurements of optical and/or FIR ([O iii] 88 μm and [C ii] 158 μm) emission-line fluxes and plot them on the [O
iii
]λ5007/Hβ–[N
ii
]λ6585/Hα (BPT) and L([O iii]88)/SFR–L([C
ii
]158)/SFR diagrams, where SFR is the star formation rate and L([O
iii
]88) and L([C
ii
]158) are the FIR line luminosities. We aim to explain the galaxy distributions on the two diagrams with photoionization models that employ three nebular parameters: the ionization parameter U, hydrogen density n
H, and gaseous metallicity Z
gas. Our models successfully reproduce the nebular parameters of local galaxies, and then predict the distributions of the z ∼ 0, 2, and >6 galaxies in the diagrams. The predicted distributions illustrate the redshift evolution on all the diagrams; e.g., [O
iii
]/Hβ and [O
iii
]88/[C ii]158 ratios continuously decrease from z > 6 to 0. Specifically, the z > 6 galaxies exhibit ∼0.5 dex higher U than low-redshift galaxies at a given Z
gas and show predicted flat distributions on the BPT diagram at
log
[
O
III
]
/
H
β
=
0.5–0.8. We find that some of the z > 6 galaxies exhibit high L([O iii]88)/SFR ratios. To explain these high ratios, our photoionization models require a low stellar-to-gaseous-metallicity ratio or bursty/increasing star formation history at z > 6. JWST will test the predictions and scenarios for the z > 6 galaxies proposed by our photoionization modeling.