Subsurface stratigraphy is an indispensable component of geotechnical site characterization and primarily deals with the interpretation of geological interfaces from site-specific measurements, such as boreholes. Traditional geological profiling methods often rely on engineering judgement for manual drawing or entirely depend on parametric models for interpolation. Both approaches face challenges when dealing with limited geo-data. To effectively address the dilemma, a new machine learning paradigm is proposed in this study to combine valuable prior geological knowledge and sparse site-specific measurements for data-driven predictions of both two-dimensional geological cross-sections and three-dimensional geological domains. The valuable prior knowledge is quantitatively represented as training images, which are compiled and stored in a training image database that is further enriched and augmented by employing deep generative models. Subsequently, the optimal training images that are compatible with the available site-specific data are adaptively selected for onward stochastic predictions under the framework of non-parametric Bayesian analysis. The method has been successfully applied to tackle geological profiling challenges in Hong Kong. The proposed framework is demonstrated to be capable of not only predicting the most probable geological patterns but also effectively quantifying associated stratigraphic uncertainty. The framework holds great potential of revolutionizing current engineering practices.