SWORD: Scene-Grounded Wasserstein Object-Relation Distance for 3D Scene Graph Prediction

3D scene graph prediction is commonly supervised with local object and predicate classification losses. Although effective for slot-wise label prediction, this formulation does not provide a graph-level semantic distance between a predicted scene graph and its ground truth: semantically mild label errors and structurally disruptive relational errors can be treated similarly, and subject-predicate-object facts are not compared as scene-level units. We propose Contextual Hellinger Triplet Geometry, a graph-level supervision objective that measures the semantic and structural discrepancy between 3D scene graphs. Our key idea is to reinterpret the conventional classifier outputs of a 3D scene graph predictor as an aligned probabilistic scene graph field, where object and predicate predictions jointly define contextual subject-predicate-object facts. This formulation yields a differentiable metric-based training objective with an efficient factorized implementation and can be applied to existing 3D scene graph prediction architectures without modifying their network design. Experiments on 3DSSG demonstrate that our supervision improves downstream graph-conditioned 3D scene generation, while ablation studies confirm the complementary roles of the proposed graph-level terms and user studies show better graph descriptiveness, relation plausibility, and structural preservation.

3D scene graphs provide a structured representation of complex environments by encoding objects, their semantic attributes, and the spatial and functional relationships between them. Current approaches for 3D scene graph generation suffer from several fundamental limitations. They rely on complex multi-stage pipelines with explicit intermediate representations, making systems fragile and prone to error propagation. They assume access to ground-truth object annotations during inference, which deviates from real-world scenarios. They depend on proprietary models, hindering open-source deployment, or incur prohibitively slow inference. We present GraphWrit3R, a simple end-to-end method that takes a 3D point cloud, Gaussian Splats, or a combination of both as input, and directly outputs a complete scene graph as a structured JSON script. The graph lists all objects, their semantic attributes, and the relationships between them, while avoiding all of the above mentioned limitations. The choice of multiple input modalities is purely for versatility, allowing a single set of weights to handle diverse scenarios. Point cloud inputs are encoded via Sonata and Gaussian Splat inputs via Chorus, with both modalities projected onto a shared voxel grid and fused through a novel per-voxel contrastive alignment loss before being decoded by a large language model. As a natural consequence of the LLM, GraphWrit3R also supports open-vocabulary querying. On the 3DSSG benchmark, our method achieves state-of-the-art performance on object class, predicate, and triplet recall, outperforming methods that rely on ground-truth object annotations during inference. We further provide qualitative results and analyze different input modality configurations, contrastive loss formulations, and token fusion strategies.

3D scene graph generation requires understanding both object semantics and metric spatial relations. However, existing open-vocabulary methods often struggle with spatial predicates because language similarity reflects semantic co-occurrence rather than explicit geometry. We propose GHOST, a Geometry-constrained Hybrid diffusion framework for Open-vocabulary 3D Scene graph generaTion. GHOST jointly models continuous node geometry and discrete edge predicates, following a geometry-to-constraint-to-predicate denoising process to ensure geometrically consistent relation prediction. It introduces language-grounded constraint induction, which maps predicate embeddings to differentiable geometric constraints that guide both layout refinement and predicate reweighting. A Geometry-Topology Collaborative Denoiser further couples node and edge reasoning through noise-adaptive interaction and orientation-aware modeling. Experiments on 3DSSG demonstrate state-of-the-art performance in both closed-set and open-vocabulary settings, including over 17-point gains over RelationField on spatial predicates.