Implicit Structural Modeling via Generative Diffusion Framework

Implicit structural modeling provides a principled way to represent subsurface structure with a continuous scalar field, supporting interpretation of architecture, reconstruction of deformation history, and quantitative analysis of geological processes. Yet the problem is inherently challenging in tectonically complex settings. Sparse horizon and fault constraints can admit multiple plausible solutions, and standard optimization, interpolation, or regression often yields fields that violate stratigraphic continuity, distort topology near intersections and branches, or produce kinematically implausible geometries in fold-thrust belts. We address these challenges with a diffusion framework that learns a conditional distribution of admissible structural fields from simulation based examples. Despite training on stylized normal fault scenarios, the approach transfers to diverse deformation styles, including strike-slip systems and flower structures, while remaining stable in fold-thrust belts where non monotonicity and abrupt depth jumps are common. As a result, the method produces geologically coherent implicit models that better respect structural constraints and uncertainty.