We report the discovery of a well-defined correlation between B-band face-on central optical depth due to dust, τ f B , and the stellar mass surface density, μ*, of nearby (z ≤ 0.13) spiral galaxies: log(τ f B) = 1.12 (±0.11) . log(μ * /M ⊙ kpc -2 ) - 8.6(±0.8) This relation was derived from a sample of spiral galaxies taken from the Galaxy and Mass Assembly (GAMA) survey, which were detected in the FIR/submillimeter (submm) in the Herschel-ATLAS science demonstration phase field. Using a quantitative analysis of the NUV attenuation-inclination relation for complete samples of GAMA spirals categorized according to stellar mass surface density, we demonstrate that this correlation can be used to statistically correct for dust attenuation purely on the basis of optical photometry and Sérsic-profile morphological fits. Considered together with previously established empirical relationships of stellar mass to metallicity and gas mass, the near linearity and high constant of proportionality of the τ f B - μ * μ((τ f b) relation disfavors a stellar origin for the bulk of refractory grains in spiral galaxies, instead being consistent with the existence of a ubiquitous and very rapid mechanism for the growth of dust in the interstellar medium. We use the τ f B - μ* relation in conjunction with the radiation transfer model for spiral galaxies of Popescu & Tuffs to derive intrinsic scaling relations between specific star formation rate (SFR), stellar mass, and stellar surface density, in which attenuation of the UV light used for the measurement of SFR is corrected on an object-to-object basis. A marked reduction in scatter in these relations is achieved which we demonstrate is due to correction of both the inclination-dependent and face-on components of attenuation. Our results are consistent with a general picture of spiral galaxies in which most of the submm emission originates from grains residing in translucent structures, exposed to UV in the diffuse interstellar radiation field.