OT-MeanFlow3D: Bridging Optimal Transport and Meanflow for Efficient 3D Point Cloud Generation

Generating high-quality 3D point clouds requires capturing both global shape topology and local geometric details. Existing flow-based methods rely on continuous normalizing flows (CNFs) that demand expensive ODE solving and trace estimation during training, while diffusion models require hundreds of iterative denoising steps. Moreover, most approaches adopt single-level generation directly in point space, disregarding the hierarchical structure natural to 3D shapes. We propose Hierarchical Flow Matching (HFM) that extends flow matching to bilevel structure for unconditional 3D point cloud generation. HFM decomposes the task into two levels via optimal-transport flow matching: a Latent Flow Matching models the global shape manifold in a compact latent space, and a Conditional Point Flow Matching reconstructs detailed point clouds conditioned on the latent code. Both flows are trained with simple MSE regression losses. The resulting straight OT paths enable efficient sampling with as few as 15 Euler steps per flow, while the structured latent space supports downstream tasks including classification. Extensive experiments on ShapeNet and ModelNet benchmarks demonstrate that HFM achieves competitive or even best performance compared with prior state-of-the-art methods.

3D point clouds generation requires capturing both part-level layout and surface detail while preserving permutation equivariance. Existing latent generative models often encode an entire shape into a single vector, which limits their ability to retain part-level structure. We propose TokenFlow, a hierarchical flow matching framework that represents each shape as a set of latent tokens and couples a rectified flow over these tokens with a conditional flow over points. A bottleneck of $M \ll N$ learnable tokens aggregates global context through cross-attention at $O(NM)$ cost. On ShapeNet, TokenFlow achieves the best MMD and coverage across airplane, car, and chair, while obtaining 1-NNA comparable to the strongest baselines. On ModelNet, its learned latent set reaches the best reported linear-evaluation accuracy on ModelNet10. These results show that representing a shape as a set of latent tokens, aggregated at $O(NM)$ cost, provides an effective representation for 3D point cloud generation.

Single-image point cloud reconstruction must infer complete 3D geometry, including occluded parts, from a single RGB image. While diffusion-based reconstructors achieve high accuracy, they typically require many denoising iterations, resulting in slow and expensive inference. We propose Point-MF, a Mean-Flow-based framework for low-NFE single-image point cloud reconstruction that couples a Mean-Flow-compatible architecture with an auxiliary loss. Specifically, Point-MF operates directly in point-cloud space to learn the mean velocity field and enables one-step reconstruction with a single network function evaluation (1-NFE), without relying on VAE-based latent representations. To make Mean Flow effective under large interval jumps, Point-MF employs a Diffusion Transformer tailored to the Mean-Flow setting, conditioned on frozen DINOv3 image features via a lightweight token adapter and equipped with explicit interval/time conditioning. Moreover, we introduce Denoised Space Anchor, a set-distance auxiliary loss on the denoised-space estimate $x_θ$ induced by the predicted velocity field, to stabilize large-step generation and reduce outliers and density artifacts. On ShapeNet-R2N2 and Pix3D, Point-MF strikes a strong balance between reconstruction quality and inference speed compared to multi-step diffusion baselines and competitive feedforward models, while generating high-quality point clouds with millisecond-level latency.