Infrared Dark Clouds (IRDCs) are dark clouds seen in silhouette in mid-infrared surveys. They are thought to be the birthplace of massive stars, yet remarkably little information exists on the properties of the population as a whole (e.g., mass spectrum, spatial distribution). Genetic forward modeling is used along with the Two Micron All Sky Survey and the Besançon Galactic model to deduce the three-dimensional distribution of interstellar extinction toward previously identified IRDC candidates. This derived dust distribution can then be used to determine the distance and mass of IRDCs, independently of kinematic models of the Milky Way. Along a line of sight that crosses an IRDC, the extinction is seen to rise sharply at the distance of the cloud. Assuming a dust-to-gas ratio, the total mass of the cloud can be estimated. The method has been successfully applied to 1259 IRDCs, including over 1000 for which no distance or mass estimate currently exists. The IRDCs are seen to lie preferentially along the spiral arms and in the molecular ring of the Milky Way, reinforcing the idea that they are the birthplace of massive stars. Also, their mass spectrum is seen to follow a power law with an index of –1.75 ± 0.06, steeper than giant molecular clouds (GMCs) in the inner Galaxy but comparable to clumps in GMCs. This slope suggests that the IRDCs detected using the present method are not gravitationally bound, but are rather the result of density fluctuations induced by turbulence.