LATO.2：分解式三維網格生成與頂點及拓撲流

摘要

基於精心設計的潛在表示的流匹配（Flow Matching）近期已成為一種強大的拓撲感知網格生成範式。然而，現有方法將頂點與連通性共同建模於一個聯合潛在空間中，使連續的頂點幾何與離散的組合結構糾纏在一起；這使得流學習變得複雜，並表現為頂點漂移與表面斷裂。我們提出 LATO.2，一種分解式流匹配框架，將網格生成分解為一個頂點流，隨後再進行一個以已生成頂點為條件的連通性流，且兩個階段均錨定於共享的粗略體素支架。專用的變分自編碼器（VAE）支撐這兩個階段，以子體素精度重建頂點，並將離散的連通性嵌入連續的潛在空間。我們展示了這種分解方式獨有的兩項優勢：(i) 逐部分生成：將支架分割，每個部分以完整的潛在容量合成，從而產生遠比單一整體潛在空間所允許的更高解析度網格；(ii) 拓撲自適應編輯：操縱第一階段的頂點，無需重新最佳化即可誘發對應的連通性。實驗表明，LATO.2 在幾何保真度與連通性品質上超越了當前最先進的拓撲感知網格生成器。

English

Flow matching over carefully designed latent representations has recently emerged as a powerful paradigm for topology-aware mesh generation. Existing approaches, however, model vertices and connectivity jointly in a joint latent space, entangling continuous vertex geometry with discrete combinatorial structure; this complicates flow learning and manifests as drifting vertices and broken surfaces. We present LATO.2, a factorized flow matching framework that decomposes mesh generation into a vertex flow followed by a connectivity flow conditioned on the realized vertices, with both stages anchored to a shared coarse voxel scaffold. Dedicated VAEs underpin the two stages, recovering vertices at sub-voxel precision and embedding discrete connectivity into a continuous latent space. We demonstrate two advantages unique to this factorization: (i) part-wise generation, in which the scaffold is partitioned and each part synthesized at full latent capacity, yielding substantially higher-resolution meshes than a monolithic latent permits; and (ii) topology-adaptive editing, in which manipulating first-stage vertices induces the corresponding connectivity without re-optimization. Experiments show that LATO.2 surpasses state-of-the-art topology-aware mesh generators in geometric fidelity and connectivity quality.