DeltaFlow: Single-Stage Mesh Generation using Flow Matching with Laplacian Positional Encoding

Triangle meshes remain the standard 3D representation for graphics and rendering. However, current explicit triangle mesh generation methods either rely on slow autoregressive methods that generate one triangle at a time or require a multi-stage pipeline with diffusion models that hinders optimization for downstream objectives. To fill this gap, we introduce DeltaFlow, a single-stage flow matching framework for unordered triangle soups using a Diffusion Transformer (DiT) architecture. Naive triangle soup generation uses unordered tokens to represent the generated triangles, leading to meshes with duplicated or missing triangles and poor connectivity. Instead, DeltaFlow introduces Laplacian positional encoding that encodes a mesh's dual-graph Laplacian coordinates onto a shared template for rotary position embeddings (RoPE), injecting a connectivity prior into the denoising process. Experiments show that DeltaFlow generates meshes of similar quality to those generated by other mesh generative methods and substantially tighter meshes than those generated by other flow-based methods. Furthermore, our native triangle flow matching model learns a generalizable prior that enables various downstream geometry processing applications, such as mesh inpainting and point-cloud-conditioned mesh generation.