# Voronoi-Assisted Optimization for Diffusing Unsigned Distance Fields from Unoriented Points

arXiv: https://arxiv.org/abs/2510.12524 · HTML: https://mlsanity.com/paper/2510.12524/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 22 of 22)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Deep Fashion3D: A Dataset and Benchmark for 3D Garment Reconstruction from Single Images](https://mlsanity.com/paper/2003.12753/) (2020)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field](https://mlsanity.com/paper/2304.11605/) (2023)
- [Orienting Point Clouds with Dipole Propagation](https://mlsanity.com/paper/2105.01604/) (2021)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [Iterative Poisson Surface Reconstruction (iPSR) for Unoriented Points](https://mlsanity.com/paper/2209.09510/) (2022)
- [The Vector Heat Method](https://mlsanity.com/paper/1805.09170/) (2018)
- [GeoUDF: Surface Reconstruction from 3D Point Clouds via Geometry-guided Distance Representation](https://mlsanity.com/paper/2211.16762/) (2022)
- [Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering](https://mlsanity.com/paper/2310.03431/) (2023)
- [Surface Extraction from Neural Unsigned Distance Fields](https://mlsanity.com/paper/2309.08878/) (2023)
- [Diffusing Winding Gradients (DWG): A Parallel and Scalable Method for 3D Reconstruction from Unoriented Point Clouds](https://mlsanity.com/paper/2405.13839/) (2024)
- [Details Enhancement in Unsigned Distance Field Learning for High-fidelity 3D Surface Reconstruction](https://mlsanity.com/paper/2406.00346/) (2024)
- [A Lightweight UDF Learning Framework for 3D Reconstruction Based on Local Shape Functions](https://mlsanity.com/paper/2407.01330/) (2024)
- [Fast and Globally Consistent Normal Orientation based on the Winding Number Normal Consistency](https://mlsanity.com/paper/2405.16634/) (2024)
- [Parallel and Scalable Heat Methods for Geodesic Distance Computation](https://mlsanity.com/paper/1812.06060/) (2018)
- [Consistent Point Orientation for Manifold Surfaces via Boundary Integration](https://mlsanity.com/paper/2407.03165/) (2024)
- [Neural Surface Detection for Unsigned Distance Fields](https://mlsanity.com/paper/2407.18381/) (2024)
- [DCUDF2: Improving Efficiency and Accuracy in Extracting Zero Level Sets from Unsigned Distance Fields](https://mlsanity.com/paper/2408.17284/) (2024)
- [A Divide-and-Conquer Approach for Global Orientation of Non-Watertight Scene-Level Point Clouds Using 0-1 Integer Optimization](https://mlsanity.com/paper/2505.23469/) (2025)

## Built on by (most cited first, 1 of 1)

- [Metric--Phase Fields: Decoupling Distance and Sign for Thin-Structure Reconstruction from Unoriented Point Clouds](https://mlsanity.com/paper/2605.25503/) (2026)

## Abstract (arXiv)

Unsigned Distance Fields (UDFs) provide a flexible representation for 3D shapes with arbitrary topology, including open and closed surfaces, orientable and non-orientable geometries, and non-manifold structures. While recent neural approaches have shown promise in learning UDFs, they often suffer from numerical instability, high computational cost, and limited controllability. We present a lightweight, network-free method, Voronoi-Assisted Optimization for Diffusing (VAD), to compute UDFs directly from unoriented point clouds. Our approach begins by assigning bi-directional normals to input points, guided by two Voronoi-based geometric criteria encoded in an energy function for optimal alignment. The aligned normals are then diffused to form an approximate UDF gradient field, which is subsequently integrated to recover the final UDF. Experiments demonstrate that VAD robustly handles watertight and open surfaces, as well as complex non-manifold and non-orientable geometries, while remaining computationally efficient and stable.