  We complement the MALATANG sample of dense gas in nearby galaxies with
archival observations of $^{12}\rm CO$ and its isotopologues to determine
scaling relations between Wide-field Infrared Survey Explorer (WISE) 12 $\mu$m
emission and molecular gas tracers at sub-kiloparsec scales. We find that 12
$\mu$m luminosity is more tightly correlated with $^{12}\rm CO$ than it is with
$^{13}\rm CO$ or dense gas tracers. Residuals between predicted and observed
$^{12}\rm CO$ are only weakly correlated with molecular gas mass surface
density ($\Sigma_{\rm mol}$) in regions where $\Sigma_{\rm mol}$ is very low
($\sim 10~{\rm M_{\odot}~pc^{-2}}$). Above this limit, the $^{12}\rm CO$
residuals show no correlations with physical conditions of molecular gas, while
$^{13}\rm CO$ residuals depend on the gas optical depth and temperature. By
analyzing differences from galaxy to galaxy, we confirm that the $^{12}\rm
CO$-12 $\mu$m relation is strong and statistically robust with respect to star
forming galaxies and AGN hosts. These results suggest that WISE 12 $\mu$m
emission can be used to trace total molecular gas instead of dense molecular
gas, likely because polycyclic aromatic hydrocarbons (PAHs, a major contributor
to WISE 12 $\mu$m~emission) may be well-mixed with the gas that is traced by
$^{12}\rm CO$. We propose that WISE 12 $\mu$m luminosity can be used to
estimate molecular gas surface density for statistical analyses of the star
formation process in galaxies.
