Distilling Unsigned Distance Function for Surface Reconstruction from 3D Gaussian Splatting

Unsigned distance fields (UDFs) are well suited for representing open surfaces, but learning them from multi-view images is challenging because ground-truth surfaces are unavailable for supervision in most cases and the gradient of a UDF is undefined on the underlying surface. Prior methods optimize UDFs with global objectives and apply gradient-based priors ignoring the non-differentiability for queries on the target surface, which leads to unstable training and over-smoothing on fine details. We address these issues by distilling a patch-based UDF prior, trained on synthetic ground truth algebraic surfaces with closed form expressions, into a lightweight student UDF inside Gaussian optimization process. We design band-limited knowledge distillation strategy that leverages a pretrained patch-based UDF predictor to provide reliable near-surface UDF supervision, enabling stable student training and the recovery of high-frequency geometric details. In addition, we introduce a visibility- and geometry-aware confidence weighting that modulates teacher influence, further steering the student toward accurate surfaces in ambiguous or weakly constrained regions. Extensive experiments on various datasets demonstrate that our approach consistently improves reconstruction accuracy while maintaining competitive efficiency compared to existing UDF- and SDF-based methods.