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tokens: (measured either by stellar light absorption A V or gas absorption H α/H β) and H 2 is due to the correlation between dust and H 2 . This method is convenient since spatially resolved extinction maps are available for large samples of galaxies thanks to optical integral-field spectroscopy surveys. However, unlike 12 μ m, extinction as measured by the Balmer decrement is only valid over a range that is limited by the signal-to-noise ratio of the H β emission line. With extreme levels of extinction, e.g. in local ultraluminous infrared galaxies, the H β line becomes invisible, so this method cannot be used. It is not yet known whether the correlation between 12 μ m and CO holds at subgalaxy scales, or how it compares with the resolved SFR–H 2 and A V –H 2 correlations. Comparing these correlations at resolved scales may give insight into the factors driving the 12 μ m–CO correlation. The WISE 12 μ m beam full width at half-maximum (FWHM) is 6.6 arcsec (Wright et al. 2010 ), which corresponds to ≤1 kpc resolution for galaxies closer than 31 Mpc. This resolution and distance range is well matched to the Extragalactic Data base for Galaxy Evolution survey (EDGE; Bolatto et al. 2017 ). EDGE is a survey of CO(1–0) in 126 nearby galaxies with 4.5 arcsec spatial resolution using the Combined Array for Research in Millimeter-wave Astronomy (CARMA). One of the main goals of EDGE was to allow studies of resolved molecular gas and optical integral-field spectroscopy data in a large sample of nearby galaxies. In this study, we use the EDGE CO and WISE data to measure the 12 μ m and CO(1–0) correlation within individual galaxies. We find that the best-fitting parameters describing this relation vary significantly among galaxies. We perform multivariate linear regression using a combination of global galaxy measurements and quantities derived from spatially resolved optical spectroscopy from the Calar Alto Legacy Integral Field Area Survey (CALIFA; Sánchez et al. 2012 , 2016 ; Walcher et al. 2014 ). This yields a set of linear functions with log Σ(H 2 ) as the dependent variable that can be used as spatially resolved estimators of H 2 surface density. These estimators can predict H 2 surface density with a root-mean-square (RMS) accuracy of ≃0.2 dex in galaxies for which 12 μ m data are available. 2 DATA AND DATA PROCESSING 2.1 Sample selection The sample is selected from the EDGE survey (Bolatto et al. 2017 , hereafter B17 ). The typical angular resolution of EDGE CO maps is 4.5 arcsec, and the typical H 2 surface density sensitivity before deprojecting galaxy inclination is 11 M ⊙ pc −2 ( B17 ). Every EDGE galaxy has optical integral field unit (IFU) data from CALIFA, allowing joint studies of the content and kinematics of cold gas (H 2 ), ionized gas, and stellar populations, all with ∼kpc spatial resolution. We processed the CO data for all 126 EDGE galaxies, and as a starting point we selected the 95 galaxies which had at least one detected pixel