# Neural Approximation of Generalized Voronoi Diagrams

arXiv: https://arxiv.org/abs/2603.26964 · HTML: https://mlsanity.com/paper/2603.26964/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 5 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 2 of 2)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Approximate Nearest-Neighbor Search for Line Segments](https://mlsanity.com/paper/2103.16071/) (2021)

## Abstract (arXiv)

We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of constructing the diagram combinatorially, VoroFields learns a continuous, differentiable surrogate whose maximizer structure induces the partition implicitly. The Voronoi cells correspond to maximizer regions of the field, with boundaries defined by equal responses between competing sites. A hierarchical decomposition reduces the combinatorial complexity by refining only near envelope transition strata. Experiments across site families and metrics demonstrate accurate recovery of cells and boundary geometry without shape-specific constructions.