Structural geologic models are widely used to represent the spatial distribution of relevant geologic features. Several techniques exist to construct these models on the basis of different assumptions and different types of geologic observations. However, two problems are prevalent when constructing models: (1) observations and assumptions, and therefore also the constructed model, are subject to uncertainties and (2) additional information is often available, but it cannot be considered directly in the geologic modeling step — although it could be used to reduce model uncertainties. The first problem has been addressed in recent work. Here we develop a conceptual approach to consider the second aspect: We combine uncertain prior information with geologically motivated likelihood functions in a Bayesian inference framework. The result is that we not only reduce uncertainties in the ensemble of generated models, but we also gain the potential to learn additional features about the model parameters. We develop an implementation of this concept in a probabilistic programming framework, in which we extend the functionality of a 3D implicit potential-field interpolation method with geologic likelihood functions. With schematic examples, we show how this combination leads to suites of models with reduced uncertainties and how it provides a deeper insight into parameter correlations. Furthermore, the integration into a hierarchical Bayesian model provides an insight into potential extensions of the method, for example, the interpolation functional itself, and other types of information, such as gravity or magnetic potential-field data. These aspects constitute promising paths for future research.