Flow Matching Reinforcement for 3D Mesh Generation via Dynamic Homing Optimization

Recent image-to-3D generation models built on flow-matching diffusion Transformers (DiT) can produce high-fidelity meshes, yet their post-training strategy remains largely unexplored. There exist several critical bottlenecks in reinforcement learning: the inherent difficulty of defining comprehensive rewards for 3D geometric quality, and the gradient interference that arises when jointly optimizing heterogeneous objectives. Inspired by the practicability of on-policy distillation (OPD) in large language models and image generation, we propose \textbf{Flow3D-OPD}, a two-stage post-training framework that introduces multi-teacher distillation into 3D geometry generation. In the first stage, we utilize the semi-policy to enhance the foundational capability of the pretrained model and then design an agentic verifier for 3D geometric quality evaluation. Based on the verifier, we could cultivate domain-specialized teacher models via direct preference optimization (DPO). In the second stage, we consolidate heterogeneous expertise into a unified student model through on-policy distillation with hard task-routing sampling and gradient accumulation, which could mitigate the gradient interference in joint optimization. Without relying on elaborate modifications, our straightforward yet effective design achieves consistent improvements across all geometric quality dimensions and surpasses all teacher models in the average metric. Extensive experiments demonstrate that our approach provides an effective paradigm for reinforcement learning in 3D 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 \textit{Latent Flow Matching} models the global shape manifold in a compact latent space, and a \textit{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.

Meshes are among the most common 3D scene representations, but directly generating meshes is challenging because the representation contains important symmetries, including permutation invariance of faces and vertices. MeshFlow learns to generate triangle meshes directly as triangle soups, avoiding the need to serialize meshes into long autoregressive sequences. We adopt equivariant optimal-transport flow matching models that respect the key symmetries of triangle soups: arbitrary permutations of faces and permutations of the vertices within each face. Toward this goal, we propose a simple yet effective modification to the Diffusion Transformer architecture, resulting in a scalable network capable of modeling a velocity field while maintaining the desired equivariance. We further introduce an optimal-transport-based training objective that improves convergence by eliminating supervision signals that violate these symmetries. MeshFlow achieves mesh quality comparable to state-of-the-art autoregressive mesh generators while providing about an 18$\times$ speedup during inference. Project page is at https://qiisun.github.io/MeshFlow/.