VHeat-UDF: Regularizing Neural Unsigned Distance Fields with Vector Heat Diffusion

We present VHeat-UDF, a method for learning unsigned distance fields regularized by vector heat diffusion. Given potentially inconsistent surface normals, vector heat diffusion propagates geometric orientation into the ambient space, providing effective regularization for UDF learning. To address singular behavior near field singularities, we introduce a rescaled vector Dirichlet energy that remains well-defined in such regions. VHeat-UDF provides accurate distance queries and robust surface reconstruction, even from incomplete or sparse inputs. Experiments comparing our approach with existing methods and scalar heat diffusion-based regularization demonstrate its effectiveness and robustness. Code will be released upon acceptance.