A Finite Difference Approximation of Second Order Regularization of Neural-SDFs

We introduce a finite-difference framework for curvature regularization in neural signed distance field (SDF) learning. Existing approaches enforce curvature priors using full Hessian information obtained via second-order automatic differentiation, which is accurate but computationally expensive. Others reduced this overhead by avoiding explicit Hessian assembly, but still required higher-order differentiation. In contrast, our method replaces these operations with lightweight finite-difference stencils that approximate second derivatives using the well known Taylor expansion with a truncation error of O(h^2), and can serve as drop-in replacements for Gaussian curvature and rank-deficiency losses. Experiments demonstrate that our finite-difference variants achieve reconstruction fidelity comparable to their automatic-differentiation counterparts, while reducing GPU memory usage and training time by up to a factor of two. Additional tests on sparse, incomplete, and non-CAD data confirm that the proposed formulation is robust and general, offering an efficient and scalable alternative for curvature-aware SDF learning.

Pro-DG: Procedural Diffusion Guidance for Architectural Facade Generation

We present Pro-DG, a framework for procedurally controllable photo-realistic facade generation that combines a procedural shape grammar with diffusion-based image synthesis. Starting from a single input image, we reconstruct its facade layout using grammar rules, then edit that structure through user-defined transformations. As facades are inherently multi-hierarchical structures, we introduce hierarchical matching procedure that aligns facade structures at different levels which is used to introduce control maps to guide a generative diffusion pipeline. This approach retains local appearance fidelity while accommodating large-scale edits such as floor duplication or window rearrangement. We provide a thorough evaluation, comparing Pro-DG against inpainting-based baselines and synthetic ground truths. Our user study and quantitative measurements indicate improved preservation of architectural identity and higher edit accuracy. Our novel method is the first to integrate neuro-symbolically derived shape-grammars for modeling with modern generative model and highlights the broader potential of such approaches for precise and controllable image manipulation.