PolyFlow：面向艺术家风格网格生成的连续拓扑嵌入流匹配

摘要

自回归Transformer通过生成符合艺术家水准的拓扑结构主导了高质量网格生成，但其固有的顺序解码机制导致计算开销显著增加，比并行生成模型慢数个数量级。另一方面，尽管连续扩散与流匹配方法在多个领域支持高效的并行合成，但无法直接应用于网格：网格连接性本质上是离散的，与标准的连续噪声注入和去噪操作不兼容。为解决这一根本性不兼容问题，我们引入了一种紧凑拓扑嵌入器，将离散的网格顶点位置和法线投影为连续逐顶点嵌入，通过时空距离阈值化即可可靠恢复原始离散邻接信息。在预训练并冻结该嵌入器后，任何原始网格均可完全转化为连续逐顶点状态空间，统一了位置、法线和隐式拓扑属性。基于这种新颖的连续网格表示，我们提出了PolyFlow——一种基于Transformer的流匹配框架，能够根据提取的点云特征实现全并行顶点状态去噪。在推理过程中，该模型通过常微分方程求解器快速完成生成，并支持通过直接指定目标顶点数对输出网格分辨率进行显式精确控制。在Toys4K基准上的广泛评估表明，PolyFlow在倒角距离和豪斯多夫距离两项指标上均超越了最先进的自回归基线方法。

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.