PolyFlow：連續拓撲嵌入流匹配用於藝術家風格網格生成

摘要

自回歸Transformer透過生成符合藝術家標準的拓撲結構，主導了高品質網格生成領域，但其固有的序列解碼方式導致龐大的計算開銷，速度比並行生成模型慢數個數量級。另一方面，雖然連續擴散與流匹配方法支援多種領域的高效並行合成，卻無法直接應用於網格：網格連接本質上是離散的，與標準的連續雜訊注入與去噪操作不相容。為解決此根本性不相容問題，我們引入一種緊湊拓撲嵌入器，將離散的網格頂點位置與法向量投影至連續的逐頂點嵌入空間，透過時空距離閾值可忠實還原原始離散鄰接資訊。在預訓練並凍結此嵌入器後，任何原始網格皆可完整轉換為統一的連續逐頂點狀態空間，涵蓋位置、法向量與隱式拓撲屬性。基於此新穎的連續網格表徵，我們提出PolyFlow——一種基於Transformer的流匹配框架，能在提取點雲特徵的條件下實現完全並行的頂點狀態去噪。推論時，本模型透過ODE求解器快速完成生成，並可透過直接指定目標頂點數量，對輸出網格解析度進行明確且精確的控制。在Toys4K基準上的廣泛評估顯示，PolyFlow在Chamfer距離與Hausdorff距離上均超越當前最佳的自回歸基準方法。

English

Autoregressive Transformers dominate high-quality mesh generation by producing artist-worthy topologies, yet their inherent sequential decoding induces substantial computational overhead, falling orders of magnitude slower than parallel generative models. On the other hand, while continuous diffusion and flow-matching methods support efficient parallel synthesis across a variety of domains, they cannot be directly applied to meshes: mesh connectivity is inherently discrete and incompatible with standard continuous noise injection and denoising operations. To resolve this fundamental incompatibility, we introduce a compact topology embedder that projects discrete mesh vertex positions and normals into continuous per-vertex embeddings, where the original discrete adjacency information can be faithfully recovered via spacetime distance thresholding. After pretraining and freezing this embedder, any raw mesh can be fully converted into a continuous per-vertex state space unifying position, normal, and implicit topological attributes. Built upon this novel continuous mesh representation, we present PolyFlow, a Transformer-based flow-matching framework that achieves fully parallel vertex state denoising conditioned on extracted point-cloud features. During inference, our model completes generation rapidly via an ODE solver, and supports explicit, precise control over output mesh resolution by directly specifying the target vertex count. Extensive evaluations on the Toys4K benchmark demonstrate that PolyFlow surpasses state-of-the-art autoregressive baselines in both Chamfer Distance and Hausdorff Distance.