Complementary to conventional and phase x-ray radiography, dark-field imaging has become central in visualizing diffusive scattering signals that come from spatially unresolved texture within an object. To date, most diffusive dark-field retrieval methods require either the acquisition of multiple images at the cost of higher radiation dose or significant amounts of computational memory and time. In this work, a simple method of x-ray diffusive dark-field retrieval is presented, applicable to any single-mask imaging setup, with only one exposure of the sample. The approach, which is based on a model of geometric and diffusive reverse-flow conservation, is implicit and noniterative. This numerically fast methodology is applied to experimental x-ray images acquired using both a random mask and a grid mask, giving high-quality reconstructions that are very stable in the presence of noise. The method should be useful for high-speed imaging and/or imaging with low-flux sources.