Researchers developed a mathematical framework based on a first-hit rendering abstraction to isolate geometry from appearance in 3D Gaussian Splatting. ^[1] The authors propose DualDiff3D, a novel 3D reconstruction framework designed to enhance the reliability of 3D Gaussian Splatting (3DGS) in scenarios with limited input views. ^[2] Researchers proposed a new framework named X-SG²S to enable simultaneous injection of 1D to 3D watermarks for copyright protection while maintaining high fidelity. ^[3] A strict identifiability window is established where surface-consistent solutions are mathematically preferred if angular capacity is bounded. ^[4] If angular capacity is unrestricted, the same images can be perfectly explained by an incorrect, opaque billboard geometry. ^[5] Existing diffusion-based methods for 3D reconstruction often fail to separate structural information from appearance consistency, leading to blur and artifacts in rendered novel views. ^[6] Extensive experiments demonstrate that the DualDiff3D approach outperforms state-of-the-art methods even in the inference-only setting. ^[7] The proposed DualDiff pipeline leverages dual diffusion priors with a Structure-Appearance Attention (SAA) module to refine low-quality novel views. ^[8]