SceneTransporter: Optimal Transport-Guided Compositional Latent Diffusion for Single-Image Structured 3D Scene Generation

We introduce SceneTransporter, an end-to-end framework for structured 3D scene generation from a single image. While existing methods generate part-level 3D objects, they often fail to organize these parts into distinct instances in open-world scenes. Through a debiased clustering probe, we reveal a critical insight: this failure stems from the lack of structural constraints within the model's internal assignment mechanism. Based on this finding, we reframe the task of structured 3D scene generation as a global correlation assignment problem. To solve this, SceneTransporter formulates and solves an entropic Optimal Transport (OT) objective within the denoising loop of the compositional DiT model. This formulation imposes two powerful structural constraints. First, the resulting transport plan gates cross-attention to enforce an exclusive, one-to-one routing of image patches to part-level 3D latents, preventing entanglement. Second, the competitive nature of the transport encourages the grouping of similar patches, a process that is further regularized by an edge-based cost, to form coherent objects and prevent fragmentation. Extensive experiments show that SceneTransporter outperforms existing methods on open-world scene generation, significantly improving instance-level coherence and geometric fidelity. Code and models will be publicly available at https://2019epwl.github.io/SceneTransporter/.

Equivariant Local Reference Frames for Unsupervised Non-rigid Point Cloud Shape Correspondence

Unsupervised non-rigid point cloud shape correspondence underpins a multitude of 3D vision tasks, yet itself is non-trivial given the exponential complexity stemming from inter-point degree-of-freedom, i.e., pose transformations. Based on the assumption of local rigidity, one solution for reducing complexity is to decompose the overall shape into independent local regions using Local Reference Frames (LRFs) that are invariant to SE(3) transformations. However, the focus solely on local structure neglects global geometric contexts, resulting in less distinctive LRFs that lack crucial semantic information necessary for effective matching. Furthermore, such complexity introduces out-of-distribution geometric contexts during inference, thus complicating generalization. To this end, we introduce 1) EquiShape, a novel structure tailored to learn pair-wise LRFs with global structural cues for both spatial and semantic consistency, and 2) LRF-Refine, an optimization strategy generally applicable to LRF-based methods, aimed at addressing the generalization challenges. Specifically, for EquiShape, we employ cross-talk within separate equivariant graph neural networks (Cross-GVP) to build long-range dependencies to compensate for the lack of semantic information in local structure modeling, deducing pair-wise independent SE(3)-equivariant LRF vectors for each point. For LRF-Refine, the optimization adjusts LRFs within specific contexts and knowledge, enhancing the geometric and semantic generalizability of point features. Our overall framework surpasses the state-of-the-art methods by a large margin on three benchmarks. Code and models will be publicly available.