PBE: A Physics-Guided Beta-Primitive Extension for Feed-Forward 3D Reconstruction

Feed-forward Gaussian reconstruction predicts renderable 3D scenes in a single pass, but its Gaussian kernels and low-order spherical harmonics offer limited flexibility in spatial shape and view-dependent appearance. Existing Beta kernels and Spherical Beta (SB) functions offer greater flexibility through adjustable spatial decay and localized angular responses. However, predicting Beta/SB parameters in a feed-forward manner is challenging because geometry and appearance require different cues, and sparse observations do not fully constrain view-dependent appearance. We propose PBE, a Physics-guided Beta-primitive Extension that addresses this problem through input-dependent base construction and residual prediction. PBE constructs single-view Beta/SB bases from predicted depth and camera parameters, and multi-view bases from depth-consistent support-view observations. Attribute-specific gates combine these bases, while learned residuals correct inaccurate estimates. PBE integrates into the primitive-parameter prediction stage of existing reconstruction models while preserving their feature backbones and single-pass inference. Trained solely on DL3DV, it consistently improves rendering quality on Depth Anything 3, VGGT-$\Omega$, YoNoSplat, and AnySplat under matched epoch budgets. Notably, Depth Anything 3 on Mip-NeRF 360 improves from $24.25$ to $26.01$ dB after five epochs without additional fine-tuning. Ablations further show that physics-informed Beta bases outperform random bases under the same residual refinement. These results jointly validate the effectiveness of PBE.