We measure the CO-to-H2 conversion factor (α
CO) in 37 galaxies at 2 kpc resolution, using the dust surface density inferred from far-infrared emission as a tracer of the gas surface density and assuming a constant dust-to-metal ratio. In total, we have ∼790 and ∼610 independent measurements of α
CO for CO (2–1) and (1–0), respectively. The mean values for α
CO (2–1) and α
CO (1–0) are
9.3
−
5.4
+
4.6
and
4.2
−
2.0
+
1.9
M
⊙
pc
−
2
(
K
km
s
−
1
)
−
1
, respectively. The CO-intensity-weighted mean is 5.69 for α
CO (2–1) and 3.33 for α
CO (1–0). We examine how α
CO scales with several physical quantities, e.g., the star formation rate (SFR), stellar mass, and dust-mass-weighted average interstellar radiation field strength (
U
¯
). Among them,
U
¯
, ΣSFR, and the integrated CO intensity (W
CO) have the strongest anticorrelation with spatially resolved α
CO. We provide linear regression results to α
CO for all quantities tested. At galaxy-integrated scales, we observe significant correlations between α
CO and W
CO, metallicity,
U
¯
, and ΣSFR. We also find that α
CO in each galaxy decreases with the stellar mass surface density (Σ⋆) in high-surface-density regions (Σ⋆ ≥ 100 M
⊙ pc−2), following the power-law relations
α
CO
(
2
–
1
)
∝
Σ
⋆
−
0.5
and
α
CO
(
1
–
0
)
∝
Σ
⋆
−
0.2
. The power-law index is insensitive to the assumed dust-to-metal ratio. We interpret the decrease in α
CO with increasing Σ⋆ as a result of higher velocity dispersion compared to isolated, self-gravitating clouds due to the additional gravitational force from stellar sources, which leads to the reduction in α
CO. The decrease in α
CO at high Σ⋆ is important for accurately assessing molecular gas content and star formation efficiency in the centers of galaxies, which bridge “Milky Way–like” to “starburst-like” conversion factors.