Implicit Structural Modeling via Generative Diffusion Frameworks

Abstract

Implicit structural modeling can support understanding subsurface spatial configurations, revealing patterns of geological evolution, and enabling quantitative simulation of geological processes, thereby offering substantial scientific and engineering value. Conventional approaches formulate it as an optimization problem or framework interpolation to fit a continuous scalar field, whereas machine learning methods typically adopt discriminative regression to directly predict implicit models. However, in complex scenarios involving fault intersections, branching, and thrust nappes, these methods still struggle to maintain topological consistency and kinematic plausibility. In this work, we develop an implicit structural modeling approach based on diffusion models. We construct a set of training data through a simulation based synthesis pipeline and design a dedicated encoder for conditional injection, allowing the conditional branch to converge rapidly while effectively reinforcing the input conditional priors throughout the diffusion process, thereby more stably propagating structural constraints. We then inject these conditional features into a backbone network pretrained on large scale natural images to enable conditional training of the diffusion model. Although our synthetic data include only a relatively stylized normal fault system, experiments demonstrate strong generalization, enabling the model to effectively handle diverse complex structural types such as strike slip faults and intricate flower fault systems. More importantly, even in challenging thrust nappe settings where the scalar field becomes non monotonic and exhibits abrupt depth discontinuities, the model can still generate reliable implicit structural models.