# FunFact: Building Probabilistic Functional 3D Scene Graphs via Factor-Graph Reasoning

arXiv: https://arxiv.org/abs/2604.03696 · HTML: https://mlsanity.com/paper/2604.03696/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 41 of its 51 references that are in the map.
- First posted on arXiv 4 Apr 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 30 of 41)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Grounding DINO: Marrying DINO with Grounded Pre-Training for Open-Set Object Detection](https://mlsanity.com/paper/2303.05499/) (2023)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Language Models as Zero-Shot Planners: Extracting Actionable Knowledge for Embodied Agents](https://mlsanity.com/paper/2201.07207/) (2022)
- [AI2-THOR: An Interactive 3D Environment for Visual AI](https://mlsanity.com/paper/1712.05474/) (2017)
- [VirtualHome: Simulating Household Activities via Programs](https://mlsanity.com/paper/1806.07011/) (2018)
- [ConceptGraphs: Open-Vocabulary 3D Scene Graphs for Perception and Planning](https://mlsanity.com/paper/2309.16650/) (2023)
- [Recognize Anything: A Strong Image Tagging Model](https://mlsanity.com/paper/2306.03514/) (2023)
- [ConceptFusion: Open-set Multimodal 3D Mapping](https://mlsanity.com/paper/2302.07241/) (2023)
- [OpenMask3D: Open-Vocabulary 3D Instance Segmentation](https://mlsanity.com/paper/2306.13631/) (2023)
- [3D Scene Graph: A Structure for Unified Semantics, 3D Space, and Camera](https://mlsanity.com/paper/1910.02527/) (2019)
- [Hierarchical Open-Vocabulary 3D Scene Graphs for Language-Grounded Robot Navigation](https://mlsanity.com/paper/2403.17846/) (2024)
- [Habitat Synthetic Scenes Dataset (HSSD-200): An Analysis of 3D Scene Scale and Realism Tradeoffs for ObjectGoal Navigation](https://mlsanity.com/paper/2306.11290/) (2023)
- [SceneGraphFusion: Incremental 3D Scene Graph Prediction from RGB-D Sequences](https://mlsanity.com/paper/2103.14898/) (2021)
- [Kimera: from SLAM to Spatial Perception with 3D Dynamic Scene Graphs](https://mlsanity.com/paper/2101.06894/) (2021)
- [SG-Nav: Online 3D Scene Graph Prompting for LLM-based Zero-shot Object Navigation](https://mlsanity.com/paper/2410.08189/) (2024)
- [Clio: Real-time Task-Driven Open-Set 3D Scene Graphs](https://mlsanity.com/paper/2404.13696/) (2024)
- [Open3DSG: Open-Vocabulary 3D Scene Graphs from Point Clouds with Queryable Objects and Open-Set Relationships](https://mlsanity.com/paper/2402.12259/) (2024)
- [3-D Scene Graph: A Sparse and Semantic Representation of Physical Environments for Intelligent Agents](https://mlsanity.com/paper/1908.04929/) (2019)
- [Language-Grounded Dynamic Scene Graphs for Interactive Object Search with Mobile Manipulation](https://mlsanity.com/paper/2403.08605/) (2024)
- [TASKOGRAPHY: Evaluating robot task planning over large 3D scene graphs](https://mlsanity.com/paper/2207.05006/) (2022)
- [Open-Vocabulary Functional 3D Scene Graphs for Real-World Indoor Spaces](https://mlsanity.com/paper/2503.19199/) (2025)
- [Incremental 3D Semantic Scene Graph Prediction from RGB Sequences](https://mlsanity.com/paper/2305.02743/) (2023)
- [Dynamic Open-Vocabulary 3D Scene Graphs for Long-term Language-Guided Mobile Manipulation](https://mlsanity.com/paper/2410.11989/) (2024)
- [Collaborative Dynamic 3D Scene Graphs for Automated Driving](https://mlsanity.com/paper/2309.06635/) (2023)

## Built on by (most cited first, 5 of 5)

- [3D Scene Graphs: Open Challenges and Future Directions](https://mlsanity.com/paper/2606.19383/) (2026)
- [FunArt: Decoding Functional Structure and Articulation from Generative 3D Latents](https://mlsanity.com/paper/2609.20673/) (2026)
- [ForceTwin: Physics-informed Digital Twins for Robotic Manipulation from Instrumented Human Interaction](https://mlsanity.com/paper/2609.21751/) (2026)
- [GraphWrit3R: End-to-End 3D Scene Graph Writing](https://mlsanity.com/paper/2609.31595/) (2026)
- [ChronoGraph: Functional 4D Scene Graphs with Vision-Language Models for Interaction Understanding and Grounded Planning](https://mlsanity.com/paper/2609.39665/) (2026)

## Abstract (arXiv)

Recent work in 3D scene understanding is moving beyond purely spatial analysis toward functional scene understanding. However, existing methods often consider functional relationships between object pairs in isolation, failing to capture the scene-wide interdependence that humans use to resolve ambiguity. We introduce FunFact, a framework for constructing probabilistic open-vocabulary functional 3D scene graphs from posed RGB-D images. FunFact first builds an object- and part-centric 3D map and uses foundation models to propose semantically plausible functional relations. These candidates are converted into factor graph variables and constrained by both LLM-derived common-sense priors and geometric priors. This formulation enables joint probabilistic inference over all functional edges and their marginals, yielding substantially better calibrated confidence scores. To benchmark this setting, we introduce FunThor, a synthetic dataset based on AI2-THOR with part-level geometry and rule-based functional annotations. Experiments on SceneFun3D, FunGraph3D, and FunThor show that FunFact improves node and relation discovery recall and significantly reduces calibration error for ambiguous relations, highlighting the benefits of holistic probabilistic modeling for functional scene understanding. See our project page at https://funfact-scenegraph.github.io/