Layerwise Deposition-Field Generative Modeling: A Process-Conditioned Framework for Three-Dimensional Generation Through Thin-Film Deposition and Surface Growth

Three-dimensional generative modeling has predominantly represented objects through explicit geometric primitives, point clouds, implicit fields, radiance fields, or learned volumetric representations. However, many physical structures are formed through sequential material deposition, surface growth, interface formation, and repeated processing operations rather than through a single geometric construction step. This paper proposes Layerwise Deposition-Field Generative Modeling (LDF-GM), a process-conditioned framework for three-dimensional generation inspired by physical vapor deposition (PVD), chemical vapor deposition (CVD), and related thin-film fabrication processes. LDF-GM represents an evolving structure using a material field, a surface-growth field, an interface state, and a sequence of deposition operations. Each operation updates the current structure according to a learned transition model conditioned on the existing surface, material properties, deposition parameters, and process history. A hierarchical latent-variable formulation jointly models the number of deposition stages, stage-specific process conditions, and the resulting three-dimensional structure. The framework supports variable layer counts, heterogeneous materials, nonuniform thickness, conformal coatings, interface-dependent growth, and accumulated surface morphology. A physics-informed objective can incorporate material conservation, geometric consistency, process-conditioned growth priors, and interface regularization. This paper provides the mathematical formulation, a practical training strategy, a generation algorithm, and an experimental protocol for evaluating the proposed method against geometry-first generative models and process-based growth simulators. Since no implementation or benchmark experiments are reported here, the method's effectiveness and novelty remain hypotheses requiring empirical validation. LDF-GM is intended to investigate whether representing three-dimensional generation as a sequence of material-deposition state transitions can improve process controllability, structural consistency, and the generation of physically plausible layered geometries.