The relationship between porosity and permeability in limestones is a fundamental constitutive equation in subsurface fluid flow modelling, and is essential in quantifying a range of geological processes. For a given porosity, the permeability of limestones varies over a range of up to five orders of magnitude. Permeability of a given rock sample depends on the total amount of pore space, characterized by porosity, as well as how the pore space is distributed within the rock, which can be expressed as a probability density function of pore sizes. We investigate in this study whether the information about pore-size distribution can be sufficiently captured by the bulk petrographical properties extracted from thin sections. We demonstrate that most of the uncertainty can be explained by variations in texture, which is defined by the mud content (mass fraction of particles less than 0.06 mm in diameter). Using mud content as a quantitative texture descriptor, we used multivariable regression and neural network models to predict permeability from porosity. For a given porosity, inclusion of mud content reduces the uncertainty in permeability prediction from five to two orders of magnitude.