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.

翻译：我们提出VoroFields——一种层次化神经场框架，用于在任意可评估的点到站点距离下逼近低维空间中有限几何站点集合的广义沃罗诺伊图。VoroFields无需组合构造该图，而是学习一个连续可微的替代函数，其最大值结构隐式诱导出划分。沃罗诺伊胞腔对应于该场的极大值区域，其边界由竞争站点间的相等响应定义。层次化分解仅通过细化近包络过渡层来降低组合复杂度。跨站点族和度量的实验表明，该方法无需特定形状的构造即可准确恢复胞腔及边界几何。