提出连续拓扑嵌入流匹配方法,实现艺术家级网格的快速并行生成。
PolyFlow: Continuous Topology Embedding Flow Matching for Artist-style Mesh Generation

- 用嵌入层将离散网格转为连续状态空间,保留拓扑信息
- 在Toys4K上性能超越自回归模型,Chamfer和Hausdorff距离更优
- 支持指定顶点数精确控制分辨率,推理速度显著提升
自回归Transformer在高质量网格生成中表现优异,但因其序列解码导致计算开销巨大,比并行生成模型慢多个数量级。而连续扩散与流匹配方法虽支持高效并行生成,却难以直接应用于网格——因网格连接关系本质离散,无法兼容标准的连续噪声注入与去噪操作。为此,我们设计了一个紧凑的拓扑嵌入器,将离散的顶点位置与法向量映射为连续的逐顶点嵌入,通过时空距离阈值可准确恢复原始邻接关系。预训练并冻结该嵌入器后,任意原始网格均可转换为统一包含位置、法向及隐式拓扑属性的连续顶点状态空间。基于此新表示,我们提出PolyFlow:一种基于Transformer的流匹配框架,实现对顶点状态的全并行去噪,并以点云特征为条件。推理时通过求解常微分方程(ODE)快速生成,且可通过直接指定目标顶点数实现对输出网格分辨率的显式精准控制。在Toys4K基准上的大量实验表明,PolyFlow在Chamfer Distance与Hausdorff Distance上均优于当前最优自回归基线。
原文摘要 · Abstract (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.
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