Daily Papers

Recently, world-action models (WAM) have emerged to bridge vision-language-action (VLA) models and world models, unifying their reasoning and instruction-following capabilities and spatio-temporal world modeling. However, existing WAM approaches often focus on modeling 2D appearance or latent representations, with limited geometric grounding-an essential element for embodied systems operating in the physical world. We present DriveDreamer-Policy, a unified driving world-action model that integrates depth generation, future video generation, and motion planning within a single modular architecture. The model employs a large language model to process language instructions, multi-view images, and actions, followed by three lightweight generators that produce depth, future video, and actions. By learning a geometry-aware world representation and using it to guide both future prediction and planning within a unified framework, the proposed model produces more coherent imagined futures and more informed driving actions, while maintaining modularity and controllable latency. Experiments on the Navsim v1 and v2 benchmarks demonstrate that DriveDreamer-Policy achieves strong performance on both closed-loop planning and world generation tasks. In particular, our model reaches 89.2 PDMS on Navsim v1 and 88.7 EPDMS on Navsim v2, outperforming existing world-model-based approaches while producing higher-quality future video and depth predictions. Ablation studies further show that explicit depth learning provides complementary benefits to video imagination and improves planning robustness.

Videos inherently represent 2D projections of a dynamic 3D world. However, our analysis suggests that video diffusion models trained solely on raw video data often fail to capture meaningful geometric-aware structure in their learned representations. To bridge this gap between video diffusion models and the underlying 3D nature of the physical world, we propose Geometry Forcing, a simple yet effective method that encourages video diffusion models to internalize latent 3D representations. Our key insight is to guide the model's intermediate representations toward geometry-aware structure by aligning them with features from a pretrained geometric foundation model. To this end, we introduce two complementary alignment objectives: Angular Alignment, which enforces directional consistency via cosine similarity, and Scale Alignment, which preserves scale-related information by regressing unnormalized geometric features from normalized diffusion representation. We evaluate Geometry Forcing on both camera view-conditioned and action-conditioned video generation tasks. Experimental results demonstrate that our method substantially improves visual quality and 3D consistency over the baseline methods. Project page: https://GeometryForcing.github.io.

High-quality 3D world models are pivotal for embodied intelligence and Artificial General Intelligence (AGI), underpinning applications such as AR/VR content creation and robotic navigation. Despite the established strong imaginative priors, current video foundation models lack explicit 3D grounding capabilities, thus being limited in both spatial consistency and their utility for downstream 3D reasoning tasks. In this work, we present FantasyWorld, a geometry-enhanced framework that augments frozen video foundation models with a trainable geometric branch, enabling joint modeling of video latents and an implicit 3D field in a single forward pass. Our approach introduces cross-branch supervision, where geometry cues guide video generation and video priors regularize 3D prediction, thus yielding consistent and generalizable 3D-aware video representations. Notably, the resulting latents from the geometric branch can potentially serve as versatile representations for downstream 3D tasks such as novel view synthesis and navigation, without requiring per-scene optimization or fine-tuning. Extensive experiments show that FantasyWorld effectively bridges video imagination and 3D perception, outperforming recent geometry-consistent baselines in multi-view coherence and style consistency. Ablation studies further confirm that these gains stem from the unified backbone and cross-branch information exchange.

Latent World Models enhance scene representation through temporal self-supervised learning, presenting a perception annotation-free paradigm for end-to-end autonomous driving. However, the reconstruction-oriented representation learning tangles perception with planning tasks, leading to suboptimal optimization for planning. To address this challenge, we propose WorldRFT, a planning-oriented latent world model framework that aligns scene representation learning with planning via a hierarchical planning decomposition and local-aware interactive refinement mechanism, augmented by reinforcement learning fine-tuning (RFT) to enhance safety-critical policy performance. Specifically, WorldRFT integrates a vision-geometry foundation model to improve 3D spatial awareness, employs hierarchical planning task decomposition to guide representation optimization, and utilizes local-aware iterative refinement to derive a planning-oriented driving policy. Furthermore, we introduce Group Relative Policy Optimization (GRPO), which applies trajectory Gaussianization and collision-aware rewards to fine-tune the driving policy, yielding systematic improvements in safety. WorldRFT achieves state-of-the-art (SOTA) performance on both open-loop nuScenes and closed-loop NavSim benchmarks. On nuScenes, it reduces collision rates by 83% (0.30% -> 0.05%). On NavSim, using camera-only sensors input, it attains competitive performance with the LiDAR-based SOTA method DiffusionDrive (87.8 vs. 88.1 PDMS).

Open-world instance-level scene understanding aims to locate and recognize unseen object categories that are not present in the annotated dataset. This task is challenging because the model needs to both localize novel 3D objects and infer their semantic categories. A key factor for the recent progress in 2D open-world perception is the availability of large-scale image-text pairs from the Internet, which cover a wide range of vocabulary concepts. However, this success is hard to replicate in 3D scenarios due to the scarcity of 3D-text pairs. To address this challenge, we propose to harness pre-trained vision-language (VL) foundation models that encode extensive knowledge from image-text pairs to generate captions for multi-view images of 3D scenes. This allows us to establish explicit associations between 3D shapes and semantic-rich captions. Moreover, to enhance the fine-grained visual-semantic representation learning from captions for object-level categorization, we design hierarchical point-caption association methods to learn semantic-aware embeddings that exploit the 3D geometry between 3D points and multi-view images. In addition, to tackle the localization challenge for novel classes in the open-world setting, we develop debiased instance localization, which involves training object grouping modules on unlabeled data using instance-level pseudo supervision. This significantly improves the generalization capabilities of instance grouping and thus the ability to accurately locate novel objects. We conduct extensive experiments on 3D semantic, instance, and panoptic segmentation tasks, covering indoor and outdoor scenes across three datasets. Our method outperforms baseline methods by a significant margin in semantic segmentation (e.g. 34.5%sim65.3%), instance segmentation (e.g. 21.8%sim54.0%) and panoptic segmentation (e.g. 14.7%sim43.3%). Code will be available.

Human driver can easily describe the complex traffic scene by visual system. Such an ability of precise perception is essential for driver's planning. To achieve this, a geometry-aware representation that quantizes the physical 3D scene into structured grid map with semantic labels per cell, termed as 3D Occupancy, would be desirable. Compared to the form of bounding box, a key insight behind occupancy is that it could capture the fine-grained details of critical obstacles in the scene, and thereby facilitate subsequent tasks. Prior or concurrent literature mainly concentrate on a single scene completion task, where we might argue that the potential of this occupancy representation might obsess broader impact. In this paper, we propose OccNet, a multi-view vision-centric pipeline with a cascade and temporal voxel decoder to reconstruct 3D occupancy. At the core of OccNet is a general occupancy embedding to represent 3D physical world. Such a descriptor could be applied towards a wide span of driving tasks, including detection, segmentation and planning. To validate the effectiveness of this new representation and our proposed algorithm, we propose OpenOcc, the first dense high-quality 3D occupancy benchmark built on top of nuScenes. Empirical experiments show that there are evident performance gain across multiple tasks, e.g., motion planning could witness a collision rate reduction by 15%-58%, demonstrating the superiority of our method.

Energy-based predictive world models provide a powerful approach for multi-step visual planning by reasoning over latent energy landscapes rather than generating pixels. However, existing approaches face two major challenges: (i) their latent representations are typically learned in Euclidean space, neglecting the underlying geometric and hierarchical structure among states, and (ii) they struggle with long-horizon prediction, which leads to rapid degradation across extended rollouts. To address these challenges, we introduce GeoWorld, a geometric world model that preserves geometric structure and hierarchical relations through a Hyperbolic JEPA, which maps latent representations from Euclidean space onto hyperbolic manifolds. We further introduce Geometric Reinforcement Learning for energy-based optimization, enabling stable multi-step planning in hyperbolic latent space. Extensive experiments on CrossTask and COIN demonstrate around 3% SR improvement in 3-step planning and 2% SR improvement in 4-step planning compared to the state-of-the-art V-JEPA 2. Project website: https://steve-zeyu-zhang.github.io/GeoWorld.

We present WorldMirror, an all-in-one, feed-forward model for versatile 3D geometric prediction tasks. Unlike existing methods constrained to image-only inputs or customized for a specific task, our framework flexibly integrates diverse geometric priors, including camera poses, intrinsics, and depth maps, while simultaneously generating multiple 3D representations: dense point clouds, multi-view depth maps, camera parameters, surface normals, and 3D Gaussians. This elegant and unified architecture leverages available prior information to resolve structural ambiguities and delivers geometrically consistent 3D outputs in a single forward pass. WorldMirror achieves state-of-the-art performance across diverse benchmarks from camera, point map, depth, and surface normal estimation to novel view synthesis, while maintaining the efficiency of feed-forward inference. Code and models will be publicly available soon.

Creating immersive and playable 3D worlds from texts or images remains a fundamental challenge in computer vision and graphics. Existing world generation approaches typically fall into two categories: video-based methods that offer rich diversity but lack 3D consistency and rendering efficiency, and 3D-based methods that provide geometric consistency but struggle with limited training data and memory-inefficient representations. To address these limitations, we present HunyuanWorld 1.0, a novel framework that combines the best of both worlds for generating immersive, explorable, and interactive 3D scenes from text and image conditions. Our approach features three key advantages: 1) 360{\deg} immersive experiences via panoramic world proxies; 2) mesh export capabilities for seamless compatibility with existing computer graphics pipelines; 3) disentangled object representations for augmented interactivity. The core of our framework is a semantically layered 3D mesh representation that leverages panoramic images as 360{\deg} world proxies for semantic-aware world decomposition and reconstruction, enabling the generation of diverse 3D worlds. Extensive experiments demonstrate that our method achieves state-of-the-art performance in generating coherent, explorable, and interactive 3D worlds while enabling versatile applications in virtual reality, physical simulation, game development, and interactive content creation.

Humans naturally perceive the geometric structure and semantic content of a 3D world as intertwined dimensions, enabling coherent and accurate understanding of complex scenes. However, most prior approaches prioritize training large geometry models for low-level 3D reconstruction and treat high-level spatial understanding in isolation, overlooking the crucial interplay between these two fundamental aspects of 3D-scene analysis, thereby limiting generalization and leading to poor performance in downstream 3D understanding tasks. Recent attempts have mitigated this issue by simply aligning 3D models with specific language models, thus restricting perception to the aligned model's capacity and limiting adaptability to downstream tasks. In this paper, we propose InstanceGrounded Geometry Transformer (IGGT), an end-to-end large unified transformer to unify the knowledge for both spatial reconstruction and instance-level contextual understanding. Specifically, we design a 3D-Consistent Contrastive Learning strategy that guides IGGT to encode a unified representation with geometric structures and instance-grounded clustering through only 2D visual inputs. This representation supports consistent lifting of 2D visual inputs into a coherent 3D scene with explicitly distinct object instances. To facilitate this task, we further construct InsScene-15K, a large-scale dataset with high-quality RGB images, poses, depth maps, and 3D-consistent instance-level mask annotations with a novel data curation pipeline.

Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in this field, much of the focus has been on single polygons, overlooking the intricate inner- and inter-polygonal relationships inherent in multipolygons. To address this gap, our study introduces a comprehensive framework specifically designed for learning representations of polygonal geometries, particularly multipolygons. Central to our approach is the incorporation of a heterogeneous visibility graph, which seamlessly integrates both inner- and inter-polygonal relationships. To enhance computational efficiency and minimize graph redundancy, we implement a heterogeneous spanning tree sampling method. Additionally, we devise a rotation-translation invariant geometric representation, ensuring broader applicability across diverse scenarios. Finally, we introduce Multipolygon-GNN, a novel model tailored to leverage the spatial and semantic heterogeneity inherent in the visibility graph. Experiments on five real-world and synthetic datasets demonstrate its ability to capture informative representations for polygonal geometries. Code and data are available at https://github.com/dyu62/PolyGNN{github.com/dyu62/PolyGNN}.

World models serve as essential building blocks toward Artificial General Intelligence (AGI), enabling intelligent agents to predict future states and plan actions by simulating complex physical interactions. However, existing interactive models primarily predict visual observations, thereby neglecting crucial hidden states like geometric structures and spatial coherence. This leads to rapid error accumulation and temporal inconsistency. To address these limitations, we introduce DeepVerse, a novel 4D interactive world model explicitly incorporating geometric predictions from previous timesteps into current predictions conditioned on actions. Experiments demonstrate that by incorporating explicit geometric constraints, DeepVerse captures richer spatio-temporal relationships and underlying physical dynamics. This capability significantly reduces drift and enhances temporal consistency, enabling the model to reliably generate extended future sequences and achieve substantial improvements in prediction accuracy, visual realism, and scene rationality. Furthermore, our method provides an effective solution for geometry-aware memory retrieval, effectively preserving long-term spatial consistency. We validate the effectiveness of DeepVerse across diverse scenarios, establishing its capacity for high-fidelity, long-horizon predictions grounded in geometry-aware dynamics.

Existing RGB-based imitation learning approaches typically employ traditional vision encoders such as ResNet or ViT, which lack explicit 3D reasoning capabilities. Recent geometry-grounded vision models, such as VGGT~wang2025vggt, provide robust spatial understanding and are promising candidates to address this limitation. This work investigates the integration of geometry-aware visual representations into robotic manipulation. Our results suggest that incorporating the geometry-aware vision encoder into imitation learning frameworks, including ACT and DP, yields up to 6.5% improvement over standard vision encoders in success rate across single- and bi-manual manipulation tasks in both simulation and real-world settings. Despite these benefits, most geometry-grounded models require high computational cost, limiting their deployment in practical robotic systems. To address this challenge, we propose eVGGT, an efficient geometry-aware encoder distilled from VGGT. eVGGT is nearly 9 times faster and 5 times smaller than VGGT, while preserving strong 3D reasoning capabilities. Code and pretrained models will be released to facilitate further research in geometry-aware robotics.

Predictive world models that simulate future observations under explicit camera control are fundamental to interactive AI. Despite rapid advances, current systems lack spatial persistence: they fail to maintain stable scene structures over long trajectories, frequently hallucinating details when cameras revisit previously observed locations. We identify that this geometric drift stems from reliance on screen-space positional embeddings, which conflict with the projective geometry required for 3D consistency. We introduce ViewRope, a geometry-aware encoding that injects camera-ray directions directly into video transformer self-attention layers. By parameterizing attention with relative ray geometry rather than pixel locality, ViewRope provides a model-native inductive bias for retrieving 3D-consistent content across temporal gaps. We further propose Geometry-Aware Frame-Sparse Attention, which exploits these geometric cues to selectively attend to relevant historical frames, improving efficiency without sacrificing memory consistency. We also present ViewBench, a diagnostic suite measuring loop-closure fidelity and geometric drift. Our results demonstrate that ViewRope substantially improves long-term consistency while reducing computational costs.

World models have emerged as a critical frontier in AI research, aiming to enhance large models by infusing them with physical dynamics and world knowledge. The core objective is to enable agents to understand, predict, and interact with complex environments. However, current research landscape remains fragmented, with approaches predominantly focused on injecting world knowledge into isolated tasks, such as visual prediction, 3D estimation, or symbol grounding, rather than establishing a unified definition or framework. While these task-specific integrations yield performance gains, they often lack the systematic coherence required for holistic world understanding. In this paper, we analyze the limitations of such fragmented approaches and propose a unified design specification for world models. We suggest that a robust world model should not be a loose collection of capabilities but a normative framework that integrally incorporates interaction, perception, symbolic reasoning, and spatial representation. This work aims to provide a structured perspective to guide future research toward more general, robust, and principled models of the world.

World modeling has become a cornerstone in AI research, enabling agents to understand, represent, and predict the dynamic environments they inhabit. While prior work largely emphasizes generative methods for 2D image and video data, they overlook the rapidly growing body of work that leverages native 3D and 4D representations such as RGB-D imagery, occupancy grids, and LiDAR point clouds for large-scale scene modeling. At the same time, the absence of a standardized definition and taxonomy for ``world models'' has led to fragmented and sometimes inconsistent claims in the literature. This survey addresses these gaps by presenting the first comprehensive review explicitly dedicated to 3D and 4D world modeling and generation. We establish precise definitions, introduce a structured taxonomy spanning video-based (VideoGen), occupancy-based (OccGen), and LiDAR-based (LiDARGen) approaches, and systematically summarize datasets and evaluation metrics tailored to 3D/4D settings. We further discuss practical applications, identify open challenges, and highlight promising research directions, aiming to provide a coherent and foundational reference for advancing the field. A systematic summary of existing literature is available at https://github.com/worldbench/survey

Visual navigation using only a single camera and a topological map has recently become an appealing alternative to methods that require additional sensors and 3D maps. This is typically achieved through an "image-relative" approach to estimating control from a given pair of current observation and subgoal image. However, image-level representations of the world have limitations because images are strictly tied to the agent's pose and embodiment. In contrast, objects, being a property of the map, offer an embodiment- and trajectory-invariant world representation. In this work, we present a new paradigm of learning "object-relative" control that exhibits several desirable characteristics: a) new routes can be traversed without strictly requiring to imitate prior experience, b) the control prediction problem can be decoupled from solving the image matching problem, and c) high invariance can be achieved in cross-embodiment deployment for variations across both training-testing and mapping-execution settings. We propose a topometric map representation in the form of a "relative" 3D scene graph, which is used to obtain more informative object-level global path planning costs. We train a local controller, dubbed "ObjectReact", conditioned directly on a high-level "WayObject Costmap" representation that eliminates the need for an explicit RGB input. We demonstrate the advantages of learning object-relative control over its image-relative counterpart across sensor height variations and multiple navigation tasks that challenge the underlying spatial understanding capability, e.g., navigating a map trajectory in the reverse direction. We further show that our sim-only policy is able to generalize well to real-world indoor environments. Code and supplementary material are accessible via project page: https://object-react.github.io/

A proper scene representation is central to the pursuit of spatial intelligence where agents can robustly reconstruct and efficiently understand 3D scenes. A scene representation is either metric, such as landmark maps in 3D reconstruction, 3D bounding boxes in object detection, or voxel grids in occupancy prediction, or topological, such as pose graphs with loop closures in SLAM or visibility graphs in SfM. In this work, we propose to build Multiview Scene Graphs (MSG) from unposed images, representing a scene topologically with interconnected place and object nodes. The task of building MSG is challenging for existing representation learning methods since it needs to jointly address both visual place recognition, object detection, and object association from images with limited fields of view and potentially large viewpoint changes. To evaluate any method tackling this task, we developed an MSG dataset and annotation based on a public 3D dataset. We also propose an evaluation metric based on the intersection-over-union score of MSG edges. Moreover, we develop a novel baseline method built on mainstream pretrained vision models, combining visual place recognition and object association into one Transformer decoder architecture. Experiments demonstrate our method has superior performance compared to existing relevant baselines.

Despite recent advances in multimodal reasoning, representing auxiliary geometric constructions remains a fundamental challenge for multimodal large language models (MLLMs). Such constructions are absent from the original diagram and must be introduced before theorems apply. Existing approaches predominantly rely on explicit construction paradigms, including text-based geometric specification, visual-token interleaving during reasoning, and tool-augmented geometric execution. However, these methods either fail to faithfully represent complex spatial relationships, incur representation mismatch between discrete symbols and continuous geometric structures, or rely on external capabilities that hinder end-to-end optimization. To address these limitations, we propose LatentGeo, a framework that learns continuous latent visual representations to internalize auxiliary geometric constructions without pixel-level rendering or external executors. We design a three-stage curriculum that progressively aligns and internalizes these latent representations through auxiliary visual supervision, followed by LaGDPO, a latent-aware reinforcement learning procedure that stabilizes latent representations during policy optimization while improving end-task correctness. To systematically evaluate construction-centric representation quality, we introduce GeoAux, a new benchmark targeting visually dependent geometry problems, and conduct experiments on GeoAux and MathVerse. Results show that LatentGeo achieves substantial gains on geometric reasoning tasks, particularly those requiring auxiliary constructions. Extensive analyses and ablation studies further validate the effectiveness of each component in our framework.

To endow machines with the ability to perceive the real-world in a three dimensional representation as we do as humans is a fundamental and long-standing topic in Artificial Intelligence. Given different types of visual inputs such as images or point clouds acquired by 2D/3D sensors, one important goal is to understand the geometric structure and semantics of the 3D environment. Traditional approaches usually leverage hand-crafted features to estimate the shape and semantics of objects or scenes. However, they are difficult to generalize to novel objects and scenarios, and struggle to overcome critical issues caused by visual occlusions. By contrast, we aim to understand scenes and the objects within them by learning general and robust representations using deep neural networks, trained on large-scale real-world 3D data. To achieve these aims, this thesis makes three core contributions from object-level 3D shape estimation from single or multiple views to scene-level semantic understanding.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

The field of 4D world modeling - aiming to jointly capture spatial geometry and temporal dynamics - has witnessed remarkable progress in recent years, driven by advances in large-scale generative models and multimodal learning. However, the development of truly general 4D world models remains fundamentally constrained by the availability of high-quality data. Existing datasets and benchmarks often lack the dynamic complexity, multi-domain diversity, and spatial-temporal annotations required to support key tasks such as 4D geometric reconstruction, future prediction, and camera-control video generation. To address this gap, we introduce OmniWorld, a large-scale, multi-domain, multi-modal dataset specifically designed for 4D world modeling. OmniWorld consists of a newly collected OmniWorld-Game dataset and several curated public datasets spanning diverse domains. Compared with existing synthetic datasets, OmniWorld-Game provides richer modality coverage, larger scale, and more realistic dynamic interactions. Based on this dataset, we establish a challenging benchmark that exposes the limitations of current state-of-the-art (SOTA) approaches in modeling complex 4D environments. Moreover, fine-tuning existing SOTA methods on OmniWorld leads to significant performance gains across 4D reconstruction and video generation tasks, strongly validating OmniWorld as a powerful resource for training and evaluation. We envision OmniWorld as a catalyst for accelerating the development of general-purpose 4D world models, ultimately advancing machines' holistic understanding of the physical world.

Localizing objects and parts from natural language in 3D space is essential for robotics, AR, and embodied AI, yet existing methods face a trade-off between the accuracy and geometric consistency of per-scene optimization and the efficiency of feed-forward inference. We present TrianguLang, a feed-forward framework for 3D localization that requires no camera calibration at inference. Unlike prior methods that treat views independently, we introduce Geometry-Aware Semantic Attention (GASA), which utilizes predicted geometry to gate cross-view feature correspondence, suppressing semantically plausible but geometrically inconsistent matches without requiring ground-truth poses. Validated on five benchmarks including ScanNet++ and uCO3D, TrianguLang achieves state-of-the-art feed-forward text-guided segmentation and localization, reducing user effort from O(N) clicks to a single text query. The model processes each frame at 1008x1008 resolution in sim57ms (sim18 FPS) without optimization, enabling practical deployment for interactive robotics and AR applications. Code and checkpoints are available at https://cwru-aism.github.io/triangulang/.

World models play a crucial role in understanding and predicting the dynamics of the world, which is essential for video generation. However, existing world models are confined to specific scenarios such as gaming or driving, limiting their ability to capture the complexity of general world dynamic environments. Therefore, we introduce WorldDreamer, a pioneering world model to foster a comprehensive comprehension of general world physics and motions, which significantly enhances the capabilities of video generation. Drawing inspiration from the success of large language models, WorldDreamer frames world modeling as an unsupervised visual sequence modeling challenge. This is achieved by mapping visual inputs to discrete tokens and predicting the masked ones. During this process, we incorporate multi-modal prompts to facilitate interaction within the world model. Our experiments show that WorldDreamer excels in generating videos across different scenarios, including natural scenes and driving environments. WorldDreamer showcases versatility in executing tasks such as text-to-video conversion, image-tovideo synthesis, and video editing. These results underscore WorldDreamer's effectiveness in capturing dynamic elements within diverse general world environments.

Generative world models are reshaping embodied AI, enabling agents to synthesize realistic 4D driving environments that look convincing but often fail physically or behaviorally. Despite rapid progress, the field still lacks a unified way to assess whether generated worlds preserve geometry, obey physics, or support reliable control. We introduce WorldLens, a full-spectrum benchmark evaluating how well a model builds, understands, and behaves within its generated world. It spans five aspects -- Generation, Reconstruction, Action-Following, Downstream Task, and Human Preference -- jointly covering visual realism, geometric consistency, physical plausibility, and functional reliability. Across these dimensions, no existing world model excels universally: those with strong textures often violate physics, while geometry-stable ones lack behavioral fidelity. To align objective metrics with human judgment, we further construct WorldLens-26K, a large-scale dataset of human-annotated videos with numerical scores and textual rationales, and develop WorldLens-Agent, an evaluation model distilled from these annotations to enable scalable, explainable scoring. Together, the benchmark, dataset, and agent form a unified ecosystem for measuring world fidelity -- standardizing how future models are judged not only by how real they look, but by how real they behave.

The popularity of pre-trained large models has revolutionized downstream tasks across diverse fields, such as language, vision, and multi-modality. To minimize the adaption cost for downstream tasks, many Parameter-Efficient Fine-Tuning (PEFT) techniques are proposed for language and 2D image pre-trained models. However, the specialized PEFT method for 3D pre-trained models is still under-explored. To this end, we introduce Point-PEFT, a novel framework for adapting point cloud pre-trained models with minimal learnable parameters. Specifically, for a pre-trained 3D model, we freeze most of its parameters, and only tune the newly added PEFT modules on downstream tasks, which consist of a Point-prior Prompt and a Geometry-aware Adapter. The Point-prior Prompt adopts a set of learnable prompt tokens, for which we propose to construct a memory bank with domain-specific knowledge, and utilize a parameter-free attention to enhance the prompt tokens. The Geometry-aware Adapter aims to aggregate point cloud features within spatial neighborhoods to capture fine-grained geometric information through local interactions. Extensive experiments indicate that our Point-PEFT can achieve better performance than the full fine-tuning on various downstream tasks, while using only 5% of the trainable parameters, demonstrating the efficiency and effectiveness of our approach. Code is released at https://github.com/Ivan-Tang-3D/Point-PEFT.

Generative models have achieved success in producing semantically plausible 2D images, but it remains challenging in 3D generation due to the absence of spatial geometry constraints. Typically, existing methods utilize geometric features as conditions to enhance spatial awareness. However, these methods can only model relative relationships and are prone to scale inconsistency of absolute geometry. Thus, we argue that semantic information and absolute geometry empower 3D cognition, thereby enabling controllable 3D generation for the physical world. In this work, we propose Cog2Gen3D, a 3D cognition-guided diffusion framework for 3D generation. Our model is guided by three key designs: 1) Cognitive Feature Embeddings. We encode different modalities into semantic and geometric representations and further extract logical representations. 2) 3D Latent Cognition Graph. We structure different representations into dual-stream semantic-geometric graphs and fuse them via common-based cross-attention to obtain a 3D cognition graph. 3) Cognition-Guided Latent Diffusion. We leverage the fused 3D cognition graph as the condition to guide the latent diffusion process for 3D Gaussian generation. Under this unified framework, the 3D cognition graph ensures the physical plausibility and structural rationality of 3D generation. Moreover, we construct a validation subset based on the Marble World Labs. Extensive experiments demonstrate that our Cog2Gen3D significantly outperforms existing methods in both semantic fidelity and geometric plausibility.

Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume. Notably, our representation does not rely on a regular grid, is supervised directly by the target surface alone, and also handles open surfaces with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids and show that our method surpasses recent state-of-the-art techniques in terms of both surface and edge-based metrics.

Multimodal large language models (MLLMs) have made rapid progress in recent years, yet continue to struggle with low-level visual perception (LLVP) -- particularly the ability to accurately describe the geometric details of an image. This capability is crucial for applications in areas such as robotics, medical image analysis, and manufacturing. In this paper, we first introduce Geoperception, a benchmark designed to evaluate an MLLM's ability to accurately transcribe 2D geometric information from an image. Using this benchmark, we demonstrate the limitations of leading MLLMs, and then conduct a comprehensive empirical study to explore strategies for improving their performance on geometric tasks. Our findings highlight the benefits of certain model architectures, training techniques, and data strategies, including the use of high-fidelity synthetic data and multi-stage training with a data curriculum. Notably, we find that a data curriculum enables models to learn challenging geometry understanding tasks which they fail to learn from scratch. Leveraging these insights, we develop Euclid, a family of models specifically optimized for strong low-level geometric perception. Although purely trained on synthetic multimodal data, Euclid shows strong generalization ability to novel geometry shapes. For instance, Euclid outperforms the best closed-source model, Gemini-1.5-Pro, by up to 58.56% on certain Geoperception benchmark tasks and 10.65% on average across all tasks.

The integration of geometric reconstruction and generative modeling remains a critical challenge in developing AI systems capable of human-like spatial reasoning. This paper proposes Aether, a unified framework that enables geometry-aware reasoning in world models by jointly optimizing three core capabilities: (1) 4D dynamic reconstruction, (2) action-conditioned video prediction, and (3) goal-conditioned visual planning. Through task-interleaved feature learning, Aether achieves synergistic knowledge sharing across reconstruction, prediction, and planning objectives. Building upon video generation models, our framework demonstrates unprecedented synthetic-to-real generalization despite never observing real-world data during training. Furthermore, our approach achieves zero-shot generalization in both action following and reconstruction tasks, thanks to its intrinsic geometric modeling. Remarkably, even without real-world data, its reconstruction performance far exceeds that of domain-specific models. Additionally, Aether leverages a geometry-informed action space to seamlessly translate predictions into actions, enabling effective autonomous trajectory planning. We hope our work inspires the community to explore new frontiers in physically-reasonable world modeling and its applications.

For robots to perform a wide variety of tasks, they require a 3D representation of the world that is semantically rich, yet compact and efficient for task-driven perception and planning. Recent approaches have attempted to leverage features from large vision-language models to encode semantics in 3D representations. However, these approaches tend to produce maps with per-point feature vectors, which do not scale well in larger environments, nor do they contain semantic spatial relationships between entities in the environment, which are useful for downstream planning. In this work, we propose ConceptGraphs, an open-vocabulary graph-structured representation for 3D scenes. ConceptGraphs is built by leveraging 2D foundation models and fusing their output to 3D by multi-view association. The resulting representations generalize to novel semantic classes, without the need to collect large 3D datasets or finetune models. We demonstrate the utility of this representation through a number of downstream planning tasks that are specified through abstract (language) prompts and require complex reasoning over spatial and semantic concepts. (Project page: https://concept-graphs.github.io/ Explainer video: https://youtu.be/mRhNkQwRYnc )

We investigate a challenging task of dynamic scene geometry estimation, which requires representing both spatial and temporal features. Typically, existing methods align the two features into a unified latent space to model scene geometry. However, this unified paradigm suffers from potential mismatched representation due to the heterogeneous nature between spatial and temporal features. In this work, we propose 4D-VGGT, a general foundation model with divide-and-conquer spatiotemporal representation for dynamic scene geometry. Our model is divided into three aspects: 1) Multi-setting input. We design an adaptive visual grid that supports input sequences with arbitrary numbers of views and time steps. 2) Multi-level representation. We propose a cross-view global fusion for spatial representation and a cross-time local fusion for temporal representation. 3) Multi-task prediction. We append multiple task-specific heads to spatiotemporal representations, enabling a comprehensive visual geometry estimation for dynamic scenes. Under this unified framework, these components enhance the feature discriminability and application universality of our model for dynamic scenes. In addition, we integrate multiple geometry datasets to train our model and conduct extensive experiments to verify the effectiveness of our method across various tasks on multiple dynamic scene geometry benchmarks.

Empowered by large-scale training, vision-language models (VLMs) achieve strong image and video understanding, yet their ability to perform spatial reasoning in both static scenes and dynamic videos remains limited. Recent advances try to handle this limitation by injecting geometry tokens from pretrained 3D foundation models into VLMs. Nevertheless, we observe that naive token fusion followed by standard fine-tuning in this line of work often leaves such geometric cues underutilized for spatial reasoning, as VLMs tend to rely heavily on 2D visual cues. In this paper, we propose GeoSR, a framework designed to make geometry matter by encouraging VLMs to actively reason with geometry tokens. GeoSR introduces two key components: (1) Geometry-Unleashing Masking, which strategically masks portions of 2D vision tokens during training to weaken non-geometric shortcuts and force the model to consult geometry tokens for spatial reasoning; and (2) Geometry-Guided Fusion, a gated routing mechanism that adaptively amplifies geometry token contributions in regions where geometric evidence is critical. Together, these designs unleash the potential of geometry tokens for spatial reasoning tasks. Extensive experiments on both static and dynamic spatial reasoning benchmarks demonstrate that GeoSR consistently outperforms prior methods and establishes new state-of-the-art performance by effectively leveraging geometric information. The project page is available at https://suhzhang.github.io/GeoSR/.

In this paper, we propose a simple and general framework for self-supervised point cloud representation learning. Human beings understand the 3D world by extracting two levels of information and establishing the relationship between them. One is the global shape of an object, and the other is the local structures of it. However, few existing studies in point cloud representation learning explored how to learn both global shapes and local-to-global relationships without a specified network architecture. Inspired by how human beings understand the world, we utilize knowledge distillation to learn both global shape information and the relationship between global shape and local structures. At the same time, we combine contrastive learning with knowledge distillation to make the teacher network be better updated. Our method achieves the state-of-the-art performance on linear classification and multiple other downstream tasks. Especially, we develop a variant of ViT for 3D point cloud feature extraction, which also achieves comparable results with existing backbones when combined with our framework, and visualization of the attention maps show that our model does understand the point cloud by combining the global shape information and multiple local structural information, which is consistent with the inspiration of our representation learning method. Our code will be released soon.

This work investigates the fundamental fragility of state-of-the-art Vision-Language Models (VLMs) under basic geometric transformations. While modern VLMs excel at semantic tasks such as recognizing objects in canonical orientations and describing complex scenes, they exhibit systematic failures at a more fundamental level: lack of robust spatial invariance and equivariance required to reliably determine object identity under simple rotations, scaling, and identity transformations. We demonstrate this limitation through a systematic evaluation across diverse visual domains, including symbolic sketches, natural photographs, and abstract art. Performance drops sharply as semantic content becomes sparse, and this behavior is observed across architectures, model capacities, and prompting strategies. Overall, our results reveal a systematic gap between semantic understanding and spatial reasoning in current VLMs, highlighting the need for stronger geometric grounding in future multimodal systems.

Multimodal large language models (MLLMs) have made significant progress in integrating visual and linguistic understanding. Existing benchmarks typically focus on high-level semantic capabilities, such as scene understanding and visual reasoning, but often overlook a crucial, foundational ability: geometric perception. Geometric perception involves understanding geometric shapes, structures, and spatial relationships, which are essential for supporting higher-level semantic tasks. Despite its importance, this capability remains underexplored in current MLLM research. To address this gap, we introduce GePBench, a novel benchmark designed to assess the geometric perception abilities of MLLMs. Our extensive evaluations reveal that current state-of-the-art MLLMs exhibit significant deficiencies in geometric perception tasks. Furthermore, we show that models trained with GePBench data demonstrate substantial improvements on a wide range of benchmark tasks, highlighting the critical role of geometric perception in enabling advanced multimodal applications. Our code and datasets will be publicly available.

Visual Language Models (VLMs) have increasingly become the main paradigm for understanding indoor scenes, but they still struggle with metric and spatial reasoning. Current approaches rely on end-to-end video understanding or large-scale spatial question answering fine-tuning, inherently coupling perception and reasoning. In this paper, we investigate whether decoupling perception and reasoning leads to improved spatial reasoning. We propose an agentic framework for static 3D indoor scene reasoning that grounds an LLM in an explicit 3D scene graph (3DSG). Rather than ingesting videos directly, each scene is represented as a persistent 3DSG constructed by a dedicated perception module. To isolate reasoning performance, we instantiate the 3DSG from ground-truth annotations. The agent interacts with the scene exclusively through structured geometric tools that expose fundamental properties such as object dimensions, distances, poses, and spatial relationships. The results we obtain on the static split of VSI-Bench provide an upper bound under ideal perceptual conditions on the spatial reasoning performance, and we find that it is significantly higher than previous works, by up to 16\%, without task specific fine-tuning. Compared to base VLMs, our agentic variant achieves significantly better performance, with average improvements between 33\% to 50\%. These findings indicate that explicit geometric grounding substantially improves spatial reasoning performance, and suggest that structured representations offer a compelling alternative to purely end-to-end visual reasoning.

Vision-Language Models (VLMs) have shown remarkable performance on diverse visual and linguistic tasks, yet they remain fundamentally limited in their understanding of 3D spatial structures. We propose Geometric Distillation, a lightweight, annotation-free fine-tuning framework that injects human-inspired geometric cues into pretrained VLMs without modifying their architecture. By distilling (1) sparse correspondences, (2) relative depth relations, and (3) dense cost volumes from off-the-shelf 3D foundation models (e.g., MASt3R, VGGT), our method shapes representations to be geometry-aware while remaining compatible with natural image-text inputs. Through extensive evaluations on 3D vision-language reasoning and 3D perception benchmarks, our method consistently outperforms prior approaches, achieving improved 3D spatial reasoning with significantly lower computational cost. Our work demonstrates a scalable and efficient path to bridge 2D-trained VLMs with 3D understanding, opening up wider use in spatially grounded multimodal tasks.

We introduce GeoDANO, a geometric vision-language model (VLM) with a domain-agnostic vision encoder, for solving plane geometry problems. Although VLMs have been employed for solving geometry problems, their ability to recognize geometric features remains insufficiently analyzed. To address this gap, we propose a benchmark that evaluates the recognition of visual geometric features, including primitives such as dots and lines, and relations such as orthogonality. Our preliminary study shows that vision encoders often used in general-purpose VLMs, e.g., OpenCLIP, fail to detect these features and struggle to generalize across domains. We develop GeoCLIP, a CLIP based model trained on synthetic geometric diagram-caption pairs to overcome the limitation. Benchmark results show that GeoCLIP outperforms existing vision encoders in recognizing geometric features. We then propose our VLM, GeoDANO, which augments GeoCLIP with a domain adaptation strategy for unseen diagram styles. GeoDANO outperforms specialized methods for plane geometry problems and GPT-4o on MathVerse.

We present InSpatio-WorldFM, an open-source real-time frame model for spatial intelligence. Unlike video-based world models that rely on sequential frame generation and incur substantial latency due to window-level processing, InSpatio-WorldFM adopts a frame-based paradigm that generates each frame independently, enabling low-latency real-time spatial inference. By enforcing multi-view spatial consistency through explicit 3D anchors and implicit spatial memory, the model preserves global scene geometry while maintaining fine-grained visual details across viewpoint changes. We further introduce a progressive three-stage training pipeline that transforms a pretrained image diffusion model into a controllable frame model and finally into a real-time generator through few-step distillation. Experimental results show that InSpatio-WorldFM achieves strong multi-view consistency while supporting interactive exploration on consumer-grade GPUs, providing an efficient alternative to traditional video-based world models for real-time world simulation.

Video world models aim to simulate dynamic, real-world environments, yet existing methods struggle to provide unified and precise control over camera and multi-object motion, as videos inherently operate dynamics in the projected 2D image plane. To bridge this gap, we introduce VerseCrafter, a 4D-aware video world model that enables explicit and coherent control over both camera and object dynamics within a unified 4D geometric world state. Our approach is centered on a novel 4D Geometric Control representation, which encodes the world state through a static background point cloud and per-object 3D Gaussian trajectories. This representation captures not only an object's path but also its probabilistic 3D occupancy over time, offering a flexible, category-agnostic alternative to rigid bounding boxes or parametric models. These 4D controls are rendered into conditioning signals for a pretrained video diffusion model, enabling the generation of high-fidelity, view-consistent videos that precisely adhere to the specified dynamics. Unfortunately, another major challenge lies in the scarcity of large-scale training data with explicit 4D annotations. We address this by developing an automatic data engine that extracts the required 4D controls from in-the-wild videos, allowing us to train our model on a massive and diverse dataset.

World models have shown great utility in improving the task performance of embodied agents. While prior work largely focuses on pixel-space world models, these approaches face practical limitations in GUI settings, where predicting complex visual elements in future states is often difficult. In this work, we explore an alternative formulation of world modeling for GUI agents, where state transitions are described in natural language rather than predicting raw pixels. First, we introduce MobileWorldBench, a benchmark that evaluates the ability of vision-language models (VLMs) to function as world models for mobile GUI agents. Second, we release MobileWorld, a large-scale dataset consisting of 1.4M samples, that significantly improves the world modeling capabilities of VLMs. Finally, we propose a novel framework that integrates VLM world models into the planning framework of mobile agents, demonstrating that semantic world models can directly benefit mobile agents by improving task success rates. The code and dataset is available at https://github.com/jacklishufan/MobileWorld

We present a central-peripheral vision-inspired framework (CVP), a simple yet effective multimodal model for spatial reasoning that draws inspiration from the two types of human visual fields -- central vision and peripheral vision. Existing approaches primarily rely on unstructured representations, such as point clouds, voxels, or patch features, and inject scene context implicitly via coordinate embeddings. However, this often results in limited spatial reasoning capabilities due to the lack of explicit, high-level structural understanding. To address this limitation, we introduce two complementary components into a Large Multimodal Model-based architecture: target-affinity token, analogous to central vision, that guides the model's attention toward query-relevant objects; and allocentric grid, akin to peripheral vision, that captures global scene context and spatial arrangements. These components work in tandem to enable structured, context-aware understanding of complex 3D environments. Experiments show that CVP achieves state-of-the-art performance across a range of 3D scene understanding benchmarks.

We present WonderZoom, a novel approach to generating 3D scenes with contents across multiple spatial scales from a single image. Existing 3D world generation models remain limited to single-scale synthesis and cannot produce coherent scene contents at varying granularities. The fundamental challenge is the lack of a scale-aware 3D representation capable of generating and rendering content with largely different spatial sizes. WonderZoom addresses this through two key innovations: (1) scale-adaptive Gaussian surfels for generating and real-time rendering of multi-scale 3D scenes, and (2) a progressive detail synthesizer that iteratively generates finer-scale 3D contents. Our approach enables users to "zoom into" a 3D region and auto-regressively synthesize previously non-existent fine details from landscapes to microscopic features. Experiments demonstrate that WonderZoom significantly outperforms state-of-the-art video and 3D models in both quality and alignment, enabling multi-scale 3D world creation from a single image. We show video results and an interactive viewer of generated multi-scale 3D worlds in https://wonderzoom.github.io/

We present WonderWorld, a novel framework for interactive 3D scene generation that enables users to interactively specify scene contents and layout and see the created scenes in low latency. The major challenge lies in achieving fast generation of 3D scenes. Existing scene generation approaches fall short of speed as they often require (1) progressively generating many views and depth maps, and (2) time-consuming optimization of the scene geometry representations. We introduce the Fast Layered Gaussian Surfels (FLAGS) as our scene representation and an algorithm to generate it from a single view. Our approach does not need multiple views, and it leverages a geometry-based initialization that significantly reduces optimization time. Another challenge is generating coherent geometry that allows all scenes to be connected. We introduce the guided depth diffusion that allows partial conditioning of depth estimation. WonderWorld generates connected and diverse 3D scenes in less than 10 seconds on a single A6000 GPU, enabling real-time user interaction and exploration. We demonstrate the potential of WonderWorld for user-driven content creation and exploration in virtual environments. We will release full code and software for reproducibility. Project website: https://kovenyu.com/WonderWorld/.

World model based planning has significantly improved decision-making in complex environments by enabling agents to simulate future states and make informed choices. This computational burden is particularly restrictive in robotics, where resources are severely constrained. To address this limitation, we propose a Sparse Imagination for Efficient Visual World Model Planning, which enhances computational efficiency by reducing the number of tokens processed during forward prediction. Our method leverages a sparsely trained vision-based world model based on transformers with randomized grouped attention strategy, allowing the model to flexibly adjust the number of tokens processed based on the computational resource. By enabling sparse imagination during latent rollout, our approach significantly accelerates planning while maintaining high control fidelity. Experimental results demonstrate that sparse imagination preserves task performance while dramatically improving inference efficiency. This general technique for visual planning is applicable from simple test-time trajectory optimization to complex real-world tasks with the latest VLAs, enabling the deployment of world models in real-time scenarios.

In recent years, 3D scene graphs have emerged as a powerful world representation, offering both geometric accuracy and semantic richness. Combining 3D scene graphs with large language models enables robots to reason, plan, and navigate in complex human-centered environments. However, current approaches for constructing 3D scene graphs are semantically limited to a predefined set of relationships, and their serialization in large environments can easily exceed an LLM's context window. We introduce KeySG, a framework that represents 3D scenes as a hierarchical graph consisting of floors, rooms, objects, and functional elements, where nodes are augmented with multi-modal information extracted from keyframes selected to optimize geometric and visual coverage. The keyframes allow us to efficiently leverage VLM to extract scene information, alleviating the need to explicitly model relationship edges between objects, enabling more general, task-agnostic reasoning and planning. Our approach can process complex and ambiguous queries while mitigating the scalability issues associated with large scene graphs by utilizing a hierarchical retrieval-augmented generation (RAG) pipeline to extract relevant context from the graph. Evaluated across four distinct benchmarks -- including 3D object segmentation and complex query retrieval -- KeySG outperforms prior approaches on most metrics, demonstrating its superior semantic richness and efficiency.

The concept of 3D scene graphs is increasingly recognized as a powerful semantic and hierarchical representation of the environment. Current approaches often address this at a coarse, object-level resolution. In contrast, our goal is to develop a representation that enables robots to directly interact with their environment by identifying both the location of functional interactive elements and how these can be used. To achieve this, we focus on detecting and storing objects at a finer resolution, focusing on affordance-relevant parts. The primary challenge lies in the scarcity of data that extends beyond instance-level detection and the inherent difficulty of capturing detailed object features using robotic sensors. We leverage currently available 3D resources to generate 2D data and train a detector, which is then used to augment the standard 3D scene graph generation pipeline. Through our experiments, we demonstrate that our approach achieves functional element segmentation comparable to state-of-the-art 3D models and that our augmentation enables task-driven affordance grounding with higher accuracy than the current solutions. See our project page at https://fungraph.github.io.

Diagrams serve as a fundamental form of visual language, representing complex concepts and their inter-relationships through structured symbols, shapes, and spatial arrangements. Unlike natural images, their inherently symbolic and abstract nature poses significant challenges for Multimodal Large Language Models (MLLMs). However, current benchmarks conflate perceptual and reasoning tasks, making it difficult to assess whether MLLMs genuinely understand mathematical diagrams beyond superficial pattern recognition. To address this gap, we introduce MATHGLANCE, a benchmark specifically designed to isolate and evaluate mathematical perception in MLLMs. MATHGLANCE comprises 1.2K images and 1.6K carefully curated questions spanning four perception tasks: shape classification, object counting, relationship identification, and object grounding, covering diverse domains including plane geometry, solid geometry, and graphical representations. Our evaluation of MLLMs reveals that their ability to understand diagrams is notably limited, particularly in fine-grained grounding tasks. In response, we construct GeoPeP, a perception-oriented dataset of 200K structured geometry image-text pairs explicitly annotated with geometric primitives and precise spatial relationships. Training MLLM on GeoPeP leads to significant gains in perceptual accuracy, which in turn substantially improves mathematical reasoning. Our benchmark and dataset establish critical standards for evaluating and advancing multimodal mathematical understanding, providing valuable resources and insights to foster future MLLM research.

AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the ability to identify and interpret geometric elements based on natural language queries. To address this, we introduce the task of Referring Expression Comprehension (REC) for geometric problems, which evaluates whether models can localize points, shapes, and spatial relations in diagrams in response to textual prompts. We present GeoRef, a benchmark dataset constructed from existing geometric problem corpora, featuring diverse, high-quality annotations and queries. Due to the lack of annotated data for this task, we generate a large-scale synthetic training dataset using a structured geometric formal language, enabling broad coverage of geometric concepts and facilitating model adaptation. We explore two fine-tuning approaches: Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO). Our results show that GRPO significantly outperforms SFT by better aligning model behavior with task-specific rewards. Furthermore, we propose a verify-and-regenerate mechanism that detects incorrect predictions and re-infers answers using contextual reasoning history, further boosting accuracy. Notably, even state-of-the-art Multimodal Large Language Models (MLLMs) struggle with this task, underscoring the necessity of explicitly evaluating and strengthening geometric grounding as a prerequisite for robust geometric problem solving. Moreover, models trained on GeoRef demonstrate measurable improvements on downstream geometric reasoning tasks, highlighting the broader value of REC as a foundation for multimodal mathematical understanding.

For robots to robustly understand and interact with the physical world, it is highly beneficial to have a comprehensive representation - modelling geometry, physics, and visual observations - that informs perception, planning, and control algorithms. We propose a novel dual Gaussian-Particle representation that models the physical world while (i) enabling predictive simulation of future states and (ii) allowing online correction from visual observations in a dynamic world. Our representation comprises particles that capture the geometrical aspect of objects in the world and can be used alongside a particle-based physics system to anticipate physically plausible future states. Attached to these particles are 3D Gaussians that render images from any viewpoint through a splatting process thus capturing the visual state. By comparing the predicted and observed images, our approach generates visual forces that correct the particle positions while respecting known physical constraints. By integrating predictive physical modelling with continuous visually-derived corrections, our unified representation reasons about the present and future while synchronizing with reality. Our system runs in realtime at 30Hz using only 3 cameras. We validate our approach on 2D and 3D tracking tasks as well as photometric reconstruction quality. Videos are found at https://embodied-gaussians.github.io/.

As transformers are equivariant to the permutation of input tokens, encoding the positional information of tokens is necessary for many tasks. However, since existing positional encoding schemes have been initially designed for NLP tasks, their suitability for vision tasks, which typically exhibit different structural properties in their data, is questionable. We argue that existing positional encoding schemes are suboptimal for 3D vision tasks, as they do not respect their underlying 3D geometric structure. Based on this hypothesis, we propose a geometry-aware attention mechanism that encodes the geometric structure of tokens as relative transformation determined by the geometric relationship between queries and key-value pairs. By evaluating on multiple novel view synthesis (NVS) datasets in the sparse wide-baseline multi-view setting, we show that our attention, called Geometric Transform Attention (GTA), improves learning efficiency and performance of state-of-the-art transformer-based NVS models without any additional learned parameters and only minor computational overhead.

In this paper, we present a novel, scalable approach for constructing open set, instance-level 3D scene representations, advancing open world understanding of 3D environments. Existing methods require pre-constructed 3D scenes and face scalability issues due to per-point feature vector learning, limiting their efficacy with complex queries. Our method overcomes these limitations by incrementally building instance-level 3D scene representations using 2D foundation models, efficiently aggregating instance-level details such as masks, feature vectors, names, and captions. We introduce fusion schemes for feature vectors to enhance their contextual knowledge and performance on complex queries. Additionally, we explore large language models for robust automatic annotation and spatial reasoning tasks. We evaluate our proposed approach on multiple scenes from ScanNet and Replica datasets demonstrating zero-shot generalization capabilities, exceeding current state-of-the-art methods in open world 3D scene understanding.

We present UniScale, a unified, scale-aware multi-view 3D reconstruction framework for robotic applications that flexibly integrates geometric priors through a modular, semantically informed design. In vision-based robotic navigation, the accurate extraction of environmental structure from raw image sequences is critical for downstream tasks. UniScale addresses this challenge with a single feed-forward network that jointly estimates camera intrinsics and extrinsics, scale-invariant depth and point maps, and the metric scale of a scene from multi-view images, while optionally incorporating auxiliary geometric priors when available. By combining global contextual reasoning with camera-aware feature representations, UniScale is able to recover the metric-scale of the scene. In robotic settings where camera intrinsics are known, they can be easily incorporated to improve performance, with additional gains obtained when camera poses are also available. This co-design enables robust, metric-aware 3D reconstruction within a single unified model. Importantly, UniScale does not require training from scratch, and leverages world priors exhibited in pre-existing models without geometric encoding strategies, making it particularly suitable for resource-constrained robotic teams. We evaluate UniScale on multiple benchmarks, demonstrating strong generalization and consistent performance across diverse environments. We will release our implementation upon acceptance.

Neural implicit representations are drawing a lot of attention from the robotics community recently, as they are expressive, continuous and compact. However, city-scale continual implicit dense mapping based on sparse LiDAR input is still an under-explored challenge. To this end, we successfully build a city-scale continual neural mapping system with a panoptic representation that consists of environment-level and instance-level modelling. Given a stream of sparse LiDAR point cloud, it maintains a dynamic generative model that maps 3D coordinates to signed distance field (SDF) values. To address the difficulty of representing geometric information at different levels in city-scale space, we propose a tailored three-layer sampling strategy to dynamically sample the global, local and near-surface domains. Meanwhile, to realize high fidelity mapping of instance under incomplete observation, category-specific prior is introduced to better model the geometric details. We evaluate on the public SemanticKITTI dataset and demonstrate the significance of the newly proposed three-layer sampling strategy and panoptic representation, using both quantitative and qualitative results. Codes and model will be publicly available.

We are witnessing significant breakthroughs in the technology for generating 3D objects from text. Existing approaches either leverage large text-to-image models to optimize a 3D representation or train 3D generators on object-centric datasets. Generating entire scenes, however, remains very challenging as a scene contains multiple 3D objects, diverse and scattered. In this work, we introduce SceneWiz3D, a novel approach to synthesize high-fidelity 3D scenes from text. We marry the locality of objects with globality of scenes by introducing a hybrid 3D representation: explicit for objects and implicit for scenes. Remarkably, an object, being represented explicitly, can be either generated from text using conventional text-to-3D approaches, or provided by users. To configure the layout of the scene and automatically place objects, we apply the Particle Swarm Optimization technique during the optimization process. Furthermore, it is difficult for certain parts of the scene (e.g., corners, occlusion) to receive multi-view supervision, leading to inferior geometry. We incorporate an RGBD panorama diffusion model to mitigate it, resulting in high-quality geometry. Extensive evaluation supports that our approach achieves superior quality over previous approaches, enabling the generation of detailed and view-consistent 3D scenes.

We present NoReGeo, a novel benchmark designed to evaluate the intrinsic geometric understanding of large language models (LLMs) without relying on reasoning or algebraic computation. Unlike existing benchmarks that primarily assess models' proficiency in reasoning-based geometry-where solutions are derived using algebraic methods-NoReGeo focuses on evaluating whether LLMs can inherently encode spatial relationships and recognize geometric properties directly. Our benchmark comprises 2,500 trivial geometric problems spanning 25 categories, each carefully crafted to be solvable purely through native geometric understanding, assuming known object locations. We assess a range of state-of-the-art models on NoReGeo, including frontier models like GPT-4, observing that even the most advanced systems achieve an overall maximum of 65% accuracy in binary classification tasks. Further, our ablation experiments demonstrate that such geometric understanding does not emerge through fine-tuning alone, indicating that effective training for geometric comprehension requires a specialized approach from the outset. Our findings highlight a significant gap in current LLMs' ability to natively grasp geometric concepts, providing a foundation for future research toward models with true geometric cognition.

Understanding and reasoning about complex 3D environments requires structured scene representations that capture not only objects but also their semantic and spatial relationships. While recent works on 3D scene graph generation have leveraged pretrained VLMs without task-specific fine-tuning, they are largely confined to single-view settings, fail to support incremental updates as new observations arrive and lack explicit geometric grounding in 3D space, all of which are essential for embodied scenarios. In this paper, we propose, ZING-3D, a framework that leverages the vast knowledge of pretrained foundation models to enable open-vocabulary recognition and generate a rich semantic representation of the scene in a zero-shot manner while also enabling incremental updates and geometric grounding in 3D space, making it suitable for downstream robotics applications. Our approach leverages VLM reasoning to generate a rich 2D scene graph, which is grounded in 3D using depth information. Nodes represent open-vocabulary objects with features, 3D locations, and semantic context, while edges capture spatial and semantic relations with inter-object distances. Our experiments on scenes from the Replica and HM3D dataset show that ZING-3D is effective at capturing spatial and relational knowledge without the need of task-specific training.

What if a world simulation model could render not an imagined environment but a city that actually exists? Prior generative world models synthesize visually plausible yet artificial environments by imagining all content. We present Seoul World Model (SWM), a city-scale world model grounded in the real city of Seoul. SWM anchors autoregressive video generation through retrieval-augmented conditioning on nearby street-view images. However, this design introduces several challenges, including temporal misalignment between retrieved references and the dynamic target scene, limited trajectory diversity and data sparsity from vehicle-mounted captures at sparse intervals. We address these challenges through cross-temporal pairing, a large-scale synthetic dataset enabling diverse camera trajectories, and a view interpolation pipeline that synthesizes coherent training videos from sparse street-view images. We further introduce a Virtual Lookahead Sink to stabilize long-horizon generation by continuously re-grounding each chunk to a retrieved image at a future location. We evaluate SWM against recent video world models across three cities: Seoul, Busan, and Ann Arbor. SWM outperforms existing methods in generating spatially faithful, temporally consistent, long-horizon videos grounded in actual urban environments over trajectories reaching hundreds of meters, while supporting diverse camera movements and text-prompted scenario variations.

While Multimodal Large Language Models demonstrate impressive semantic capabilities, they often suffer from spatial blindness, struggling with fine-grained geometric reasoning and physical dynamics. Existing solutions typically rely on explicit 3D modalities or complex geometric scaffolding, which are limited by data scarcity and generalization challenges. In this work, we propose a paradigm shift by leveraging the implicit spatial prior within large-scale video generation models. We posit that to synthesize temporally coherent videos, these models inherently learn robust 3D structural priors and physical laws. We introduce VEGA-3D (Video Extracted Generative Awareness), a plug-and-play framework that repurposes a pre-trained video diffusion model as a Latent World Simulator. By extracting spatiotemporal features from intermediate noise levels and integrating them with semantic representations via a token-level adaptive gated fusion mechanism, we enrich MLLMs with dense geometric cues without explicit 3D supervision. Extensive experiments across 3D scene understanding, spatial reasoning, and embodied manipulation benchmarks demonstrate that our method outperforms state-of-the-art baselines, validating that generative priors provide a scalable foundation for physical-world understanding. Code is publicly available at https://github.com/H-EmbodVis/VEGA-3D.

Open-Vocabulary 3D object affordance grounding aims to anticipate ``action possibilities'' regions on 3D objects with arbitrary instructions, which is crucial for robots to generically perceive real scenarios and respond to operational changes. Existing methods focus on combining images or languages that depict interactions with 3D geometries to introduce external interaction priors. However, they are still vulnerable to a limited semantic space by failing to leverage implied invariant geometries and potential interaction intentions. Normally, humans address complex tasks through multi-step reasoning and respond to diverse situations by leveraging associative and analogical thinking. In light of this, we propose GREAT (GeometRy-intEntion collAboraTive inference) for Open-Vocabulary 3D Object Affordance Grounding, a novel framework that mines the object invariant geometry attributes and performs analogically reason in potential interaction scenarios to form affordance knowledge, fully combining the knowledge with both geometries and visual contents to ground 3D object affordance. Besides, we introduce the Point Image Affordance Dataset v2 (PIADv2), the largest 3D object affordance dataset at present to support the task. Extensive experiments demonstrate the effectiveness and superiority of GREAT. The code and dataset are available at https://yawen-shao.github.io/GREAT/.

Precise spatial understanding from multi-view images remains a fundamental challenge for Multimodal Large Language Models (MLLMs), as their visual representations are predominantly semantic and lack explicit geometric grounding. While existing approaches augment visual tokens with geometric cues from visual geometry models, their MLLM is still required to implicitly infer the underlying 3D structure of the scene from these augmented tokens, limiting its spatial reasoning capability. To address this issue, we introduce Cog3DMap, a framework that recurrently constructs an explicit 3D memory from multi-view images, where each token is grounded in 3D space and possesses both semantic and geometric information. By feeding these tokens into the MLLM, our framework enables direct reasoning over a spatially structured 3D map, achieving state-of-the-art performance on various spatial reasoning benchmarks. Code will be made publicly available.

Despite impressive progress in video generation, existing models remain limited to surface-level plausibility, lacking a coherent and unified understanding of the world. Prior approaches typically incorporate only a single form of world-related knowledge or rely on rigid alignment strategies to introduce additional knowledge. However, aligning the single world knowledge is insufficient to constitute a world model that requires jointly modeling multiple heterogeneous dimensions (e.g., physical commonsense, 3D and temporal consistency). To address this limitation, we introduce DreamWorld, a unified framework that integrates complementary world knowledge into video generators via a Joint World Modeling Paradigm, jointly predicting video pixels and features from foundation models to capture temporal dynamics, spatial geometry, and semantic consistency. However, naively optimizing these heterogeneous objectives can lead to visual instability and temporal flickering. To mitigate this issue, we propose Consistent Constraint Annealing (CCA) to progressively regulate world-level constraints during training, and Multi-Source Inner-Guidance to enforce learned world priors at inference. Extensive evaluations show that DreamWorld improves world consistency, outperforming Wan2.1 by 2.26 points on VBench. Code will be made publicly available at https://github.com/ABU121111/DreamWorld{mypink{Github}}.

World Generation Models are emerging as a cornerstone of next-generation multimodal intelligence systems. Unlike traditional 2D visual generation, World Models aim to construct realistic, dynamic, and physically consistent 3D/4D worlds from images, videos, or text. These models not only need to produce high-fidelity visual content but also maintain coherence across space, time, physics, and instruction control, enabling applications in virtual reality, autonomous driving, embodied intelligence, and content creation. However, prior benchmarks emphasize different evaluation dimensions and lack a unified assessment of world-realism capability. To systematically evaluate World Models, we introduce the 4DWorldBench, which measures models across four key dimensions: Perceptual Quality, Condition-4D Alignment, Physical Realism, and 4D Consistency. The benchmark covers tasks such as Image-to-3D/4D, Video-to-4D, Text-to-3D/4D. Beyond these, we innovatively introduce adaptive conditioning across multiple modalities, which not only integrates but also extends traditional evaluation paradigms. To accommodate different modality-conditioned inputs, we map all modality conditions into a unified textual space during evaluation, and further integrate LLM-as-judge, MLLM-as-judge, and traditional network-based methods. This unified and adaptive design enables more comprehensive and consistent evaluation of alignment, physical realism, and cross-modal coherence. Preliminary human studies further demonstrate that our adaptive tool selection achieves closer agreement with subjective human judgments. We hope this benchmark will serve as a foundation for objective comparisons and improvements, accelerating the transition from "visual generation" to "world generation." Our project can be found at https://yeppp27.github.io/4DWorldBench.github.io/.

Vision-Language Models (VLMs) still lack robustness in spatial intelligence, demonstrating poor performance on spatial understanding and reasoning tasks. We attribute this gap to the absence of a visual geometry learning process capable of reconstructing 3D space from 2D images. We present G^2VLM, a geometry grounded vision-language model that bridges two fundamental aspects of spatial intelligence: spatial 3D reconstruction and spatial understanding. G^2VLM natively leverages learned 3D visual geometry features to directly predict 3D attributes and enhance spatial reasoning tasks via in-context learning and interleaved reasoning. Our unified design is highly scalable for spatial understanding: it trains on abundant multi-view image and video data, while simultaneously leveraging the benefits of 3D visual priors that are typically only derived from hard-to-collect annotations. Experimental results demonstrate G^2VLM is proficient in both tasks, achieving comparable results to state-of-the-art feed-forward 3D reconstruction models and achieving better or competitive results across spatial understanding and reasoning tasks. By unifying a semantically strong VLM with low-level 3D vision tasks, we hope G^2VLM can serve as a strong baseline for the community and unlock more future applications, such as 3D scene editing.

3D room layout estimation by a single panorama using deep neural networks has made great progress. However, previous approaches can not obtain efficient geometry awareness of room layout with the only latitude of boundaries or horizon-depth. We present that using horizon-depth along with room height can obtain omnidirectional-geometry awareness of room layout in both horizontal and vertical directions. In addition, we propose a planar-geometry aware loss function with normals and gradients of normals to supervise the planeness of walls and turning of corners. We propose an efficient network, LGT-Net, for room layout estimation, which contains a novel Transformer architecture called SWG-Transformer to model geometry relations. SWG-Transformer consists of (Shifted) Window Blocks and Global Blocks to combine the local and global geometry relations. Moreover, we design a novel relative position embedding of Transformer to enhance the spatial identification ability for the panorama. Experiments show that the proposed LGT-Net achieves better performance than current state-of-the-arts (SOTA) on benchmark datasets.

While pre-trained large-scale vision models have shown significant promise for semantic correspondence, their features often struggle to grasp the geometry and orientation of instances. This paper identifies the importance of being geometry-aware for semantic correspondence and reveals a limitation of the features of current foundation models under simple post-processing. We show that incorporating this information can markedly enhance semantic correspondence performance with simple but effective solutions in both zero-shot and supervised settings. We also construct a new challenging benchmark for semantic correspondence built from an existing animal pose estimation dataset, for both pre-training validating models. Our method achieves a PCK@0.10 score of 65.4 (zero-shot) and 85.6 (supervised) on the challenging SPair-71k dataset, outperforming the state of the art by 5.5p and 11.0p absolute gains, respectively. Our code and datasets are publicly available at: https://telling-left-from-right.github.io/.

The scarcity of large-scale 3D-text paired data poses a great challenge on open vocabulary 3D scene understanding, and hence it is popular to leverage internet-scale 2D data and transfer their open vocabulary capabilities to 3D models through knowledge distillation. However, the existing distillation-based 3D scene understanding approaches rely on the representation capacity of 2D models, disregarding the exploration of geometric priors and inherent representational advantages offered by 3D data. In this paper, we propose an effective approach, namely Geometry Guided Self-Distillation (GGSD), to learn superior 3D representations from 2D pre-trained models. Specifically, we first design a geometry guided distillation module to distill knowledge from 2D models, and then leverage the 3D geometric priors to alleviate the inherent noise in 2D models and enhance the representation learning process. Due to the advantages of 3D representation, the performance of the distilled 3D student model can significantly surpass that of the 2D teacher model. This motivates us to further leverage the representation advantages of 3D data through self-distillation. As a result, our proposed GGSD approach outperforms the existing open vocabulary 3D scene understanding methods by a large margin, as demonstrated by our experiments on both indoor and outdoor benchmark datasets.

Synthesizing controllable 6-DOF object manipulation trajectories in 3D environments is essential for enabling robots to interact with complex scenes, yet remains challenging due to the need for accurate spatial reasoning, physical feasibility, and multimodal scene understanding. Existing approaches often rely on 2D or partial 3D representations, limiting their ability to capture full scene geometry and constraining trajectory precision. We present GMT, a multimodal transformer framework that generates realistic and goal-directed object trajectories by jointly leveraging 3D bounding box geometry, point cloud context, semantic object categories, and target end poses. The model represents trajectories as continuous 6-DOF pose sequences and employs a tailored conditioning strategy that fuses geometric, semantic, contextual, and goaloriented information. Extensive experiments on synthetic and real-world benchmarks demonstrate that GMT outperforms state-of-the-art human motion and human-object interaction baselines, such as CHOIS and GIMO, achieving substantial gains in spatial accuracy and orientation control. Our method establishes a new benchmark for learningbased manipulation planning and shows strong generalization to diverse objects and cluttered 3D environments. Project page: https://huajian- zeng.github. io/projects/gmt/.

World models aim to endow AI systems with the ability to represent, generate, and interact with dynamic environments in a coherent and temporally consistent manner. While recent video generation models have demonstrated impressive visual quality, they remain limited in real-time interaction, long-horizon consistency, and persistent memory of dynamic scenes, hindering their evolution into practical world models. In this report, we present TeleWorld, a real-time multimodal 4D world modeling framework that unifies video generation, dynamic scene reconstruction, and long-term world memory within a closed-loop system. TeleWorld introduces a novel generation-reconstruction-guidance paradigm, where generated video streams are continuously reconstructed into a dynamic 4D spatio-temporal representation, which in turn guides subsequent generation to maintain spatial, temporal, and physical consistency. To support long-horizon generation with low latency, we employ an autoregressive diffusion-based video model enhanced with Macro-from-Micro Planning (MMPL)--a hierarchical planning method that reduces error accumulation from frame-level to segment-level-alongside efficient Distribution Matching Distillation (DMD), enabling real-time synthesis under practical computational budgets. Our approach achieves seamless integration of dynamic object modeling and static scene representation within a unified 4D framework, advancing world models toward practical, interactive, and computationally accessible systems. Extensive experiments demonstrate that TeleWorld achieves strong performance in both static and dynamic world understanding, long-term consistency, and real-time generation efficiency, positioning it as a practical step toward interactive, memory-enabled world models for multimodal generation and embodied intelligence.

We propose ImGeoNet, a multi-view image-based 3D object detection framework that models a 3D space by an image-induced geometry-aware voxel representation. Unlike previous methods which aggregate 2D features into 3D voxels without considering geometry, ImGeoNet learns to induce geometry from multi-view images to alleviate the confusion arising from voxels of free space, and during the inference phase, only images from multiple views are required. Besides, a powerful pre-trained 2D feature extractor can be leveraged by our representation, leading to a more robust performance. To evaluate the effectiveness of ImGeoNet, we conduct quantitative and qualitative experiments on three indoor datasets, namely ARKitScenes, ScanNetV2, and ScanNet200. The results demonstrate that ImGeoNet outperforms the current state-of-the-art multi-view image-based method, ImVoxelNet, on all three datasets in terms of detection accuracy. In addition, ImGeoNet shows great data efficiency by achieving results comparable to ImVoxelNet with 100 views while utilizing only 40 views. Furthermore, our studies indicate that our proposed image-induced geometry-aware representation can enable image-based methods to attain superior detection accuracy than the seminal point cloud-based method, VoteNet, in two practical scenarios: (1) scenarios where point clouds are sparse and noisy, such as in ARKitScenes, and (2) scenarios involve diverse object classes, particularly classes of small objects, as in the case in ScanNet200.

Recent interactive video world model methods generate scene evolution conditioned on user instructions. Although they achieve impressive results, two key limitations remain. First, they fail to fully exploit the correspondence between instruction-driven scene motion and the underlying 3D geometry, which results in structural instability under viewpoint changes. Second, they easily forget historical information during multi-step interaction, resulting in error accumulation and progressive drift in scene semantics and structure. To address these issues, we propose MagicWorld, an interactive video world model that integrates 3D geometric priors and historical retrieval. MagicWorld starts from a single scene image, employs user actions to drive dynamic scene evolution, and autoregressively synthesizes continuous scenes. We introduce the Action-Guided 3D Geometry Module (AG3D), which constructs a point cloud from the first frame of each interaction and the corresponding action, providing explicit geometric constraints for viewpoint transitions and thereby improving structural consistency. We further propose History Cache Retrieval (HCR) mechanism, which retrieves relevant historical frames during generation and injects them as conditioning signals, helping the model utilize past scene information and mitigate error accumulation. Experimental results demonstrate that MagicWorld achieves notable improvements in scene stability and continuity across interaction iterations.

Emerging world models autoregressively generate video frames in response to actions, such as camera movements and text prompts, among other control signals. Due to limited temporal context window sizes, these models often struggle to maintain scene consistency during revisits, leading to severe forgetting of previously generated environments. Inspired by the mechanisms of human memory, we introduce a novel framework to enhancing long-term consistency of video world models through a geometry-grounded long-term spatial memory. Our framework includes mechanisms to store and retrieve information from the long-term spatial memory and we curate custom datasets to train and evaluate world models with explicitly stored 3D memory mechanisms. Our evaluations show improved quality, consistency, and context length compared to relevant baselines, paving the way towards long-term consistent world generation.

Geometry problem-solving (GPS), a challenging task requiring both visual comprehension and symbolic reasoning, effectively measures the reasoning capabilities of multimodal large language models (MLLMs). Humans exhibit strong reasoning ability in this task through accurate identification and adaptive application of geometric principles within visual contexts. However, existing benchmarks fail to jointly assess both dimensions of the human-like geometric reasoning mechanism in MLLMs, remaining a critical gap in assessing their ability to tackle GPS. To this end, we introduce GeoSense, the first comprehensive bilingual benchmark designed to systematically evaluate the geometric reasoning abilities of MLLMs through the lens of geometric principles. GeoSense features a five-level hierarchical framework of geometric principles spanning plane and solid geometry, an intricately annotated dataset of 1,789 problems, and an innovative evaluation strategy. Through extensive experiments on GeoSense with various open-source and closed-source MLLMs, we observe that Gemini-2.0-pro-flash performs best, achieving an overall score of 65.3. Our in-depth analysis reveals that the identification and application of geometric principles remain a bottleneck for leading MLLMs, jointly hindering their reasoning abilities. These findings underscore GeoSense's potential to guide future advancements in MLLMs' geometric reasoning capabilities, paving the way for more robust and human-like reasoning in artificial intelligence.

Visual Place Recognition (VPR) aims to match query images against a database using visual cues. State-of-the-art methods aggregate features from deep backbones to form global descriptors. Optimal transport-based aggregation methods reformulate feature-to-cluster assignment as a transport problem, but the standard Sinkhorn algorithm symmetrically treats source and target marginals, limiting effectiveness when image features and cluster centers exhibit substantially different distributions. We propose an asymmetric aggregation VPR method with geometric constraints for locally aggregated descriptors, called A^2GC-VPR. Our method employs row-column normalization averaging with separate marginal calibration, enabling asymmetric matching that adapts to distributional discrepancies in visual place recognition. Geometric constraints are incorporated through learnable coordinate embeddings, computing compatibility scores fused with feature similarities, thereby promoting spatially proximal features to the same cluster and enhancing spatial awareness. Experimental results on MSLS, NordLand, and Pittsburgh datasets demonstrate superior performance, validating the effectiveness of our approach in improving matching accuracy and robustness.

Video--based world models have emerged along two dominant paradigms: video generation and 3D reconstruction. However, existing evaluation benchmarks either focus narrowly on visual fidelity and text--video alignment for generative models, or rely on static 3D reconstruction metrics that fundamentally neglect temporal dynamics. We argue that the future of world modeling lies in 4D generation, which jointly models spatial structure and temporal evolution. In this paradigm, the core capability is interactive response: the ability to faithfully reflect how interaction actions drive state transitions across space and time. Yet no existing benchmark systematically evaluates this critical dimension. To address this gap, we propose Omni--WorldBench, a comprehensive benchmark specifically designed to evaluate the interactive response capabilities of world models in 4D settings. Omni--WorldBench comprises two key components: Omni--WorldSuite, a systematic prompt suite spanning diverse interaction levels and scene types; and Omni--Metrics, an agent-based evaluation framework that quantifies world modeling capabilities by measuring the causal impact of interaction actions on both final outcomes and intermediate state evolution trajectories. We conduct extensive evaluations of 18 representative world models across multiple paradigms. Our analysis reveals critical limitations of current world models in interactive response, providing actionable insights for future research. Omni-WorldBench will be publicly released to foster progress in interactive 4D world modeling.

We tackle the challenge of generating the infinitely extendable 3D world -- large, continuous environments with coherent geometry and realistic appearance. Existing methods face key challenges: 2D-lifting approaches suffer from geometric and appearance inconsistencies across views, 3D implicit representations are hard to scale up, and current 3D foundation models are mostly object-centric, limiting their applicability to scene-level generation. Our key insight is leveraging strong generation priors from pre-trained 3D models for structured scene block generation. To this end, we propose WorldGrow, a hierarchical framework for unbounded 3D scene synthesis. Our method features three core components: (1) a data curation pipeline that extracts high-quality scene blocks for training, making the 3D structured latent representations suitable for scene generation; (2) a 3D block inpainting mechanism that enables context-aware scene extension; and (3) a coarse-to-fine generation strategy that ensures both global layout plausibility and local geometric/textural fidelity. Evaluated on the large-scale 3D-FRONT dataset, WorldGrow achieves SOTA performance in geometry reconstruction, while uniquely supporting infinite scene generation with photorealistic and structurally consistent outputs. These results highlight its capability for constructing large-scale virtual environments and potential for building future world models.

Spatial intelligence spans a rich suite of abilities, including visualising and transforming shapes, mentally rotating objects, judging relational positions and containment, and estimating numerosity. However, it still remains a critical unresolved challenge for Multimodal Large Language Models (MLLMs).To fill this gap, we propose to treat Euclidean geometry problem-solving as a surrogate task. Specifically, we meticulously constructed a curated multimodal dataset, called Euclid30K, comprising approximately 30K plane and solid geometry problems. To enable the model to acquire and apply Euclidean principles from these geometry problems, we employed Group Relative Policy Optimization (GRPO) to finetune the Qwen2.5VL family and RoboBrain2.0 family, inspiring the models to identify shapes, count, and relate entities, and perform multi-step deductive reasoning using Euclidean principles. Our experiments demonstrate that the resulting models achieve substantial zero-shot gains across four spatial reasoning benchmarks (Super-CLEVR, Omni3DBench, VSI-Bench, and MindCube) without any task-specific adaptations. Notably, after training on the Euclid30K, the mean VSI-Bench accuracy of all evaluated models rose from 34.5% to 40.5%, improving by 5.5 percentage points. Among them, RoboBrain2.0-Euclid-7B achieves 49.6\% accuracy, surpassing the previous state-of-the-art model, Spatial-MLLM.To our knowledge, this is the first systematic study showing that geometry-centric fine-tuning can confer vision-language models with broadly transferable spatial skills. Code and Euclid30K dataset can be found in https://zgca-ai4edu.github.io/Euclids_Gift.

Embodied AI requires agents that perceive, act, and anticipate how actions reshape future world states. World models serve as internal simulators that capture environment dynamics, enabling forward and counterfactual rollouts to support perception, prediction, and decision making. This survey presents a unified framework for world models in embodied AI. Specifically, we formalize the problem setting and learning objectives, and propose a three-axis taxonomy encompassing: (1) Functionality, Decision-Coupled vs. General-Purpose; (2) Temporal Modeling, Sequential Simulation and Inference vs. Global Difference Prediction; (3) Spatial Representation, Global Latent Vector, Token Feature Sequence, Spatial Latent Grid, and Decomposed Rendering Representation. We systematize data resources and metrics across robotics, autonomous driving, and general video settings, covering pixel prediction quality, state-level understanding, and task performance. Furthermore, we offer a quantitative comparison of state-of-the-art models and distill key open challenges, including the scarcity of unified datasets and the need for evaluation metrics that assess physical consistency over pixel fidelity, the trade-off between model performance and the computational efficiency required for real-time control, and the core modeling difficulty of achieving long-horizon temporal consistency while mitigating error accumulation. Finally, we maintain a curated bibliography at https://github.com/Li-Zn-H/AwesomeWorldModels.

Polygon meshes are an efficient representation of 3D geometry, and are of central importance in computer graphics, robotics and games development. Existing learning-based approaches have avoided the challenges of working with 3D meshes, instead using alternative object representations that are more compatible with neural architectures and training approaches. We present an approach which models the mesh directly, predicting mesh vertices and faces sequentially using a Transformer-based architecture. Our model can condition on a range of inputs, including object classes, voxels, and images, and because the model is probabilistic it can produce samples that capture uncertainty in ambiguous scenarios. We show that the model is capable of producing high-quality, usable meshes, and establish log-likelihood benchmarks for the mesh-modelling task. We also evaluate the conditional models on surface reconstruction metrics against alternative methods, and demonstrate competitive performance despite not training directly on this task.

Real-world robotic manipulation demands visuomotor policies capable of robust spatial scene understanding and strong generalization across diverse camera viewpoints. While recent advances in 3D-aware visual representations have shown promise, they still suffer from several key limitations, including reliance on multi-view observations during inference which is impractical in single-view restricted scenarios, incomplete scene modeling that fails to capture holistic and fine-grained geometric structures essential for precise manipulation, and lack of effective policy training strategies to retain and exploit the acquired 3D knowledge. To address these challenges, we present MethodName, a unified representation-policy learning framework for view-generalizable robotic manipulation. MethodName introduces a single-view 3D pretraining paradigm that leverages point cloud reconstruction and feed-forward gaussian splatting under multi-view supervision to learn holistic geometric representations. During policy learning, MethodName performs multi-step distillation to preserve the pretrained geometric understanding and effectively transfer it to manipulation skills. We conduct experiments on 12 RLBench tasks, where our approach outperforms the previous state-of-the-art method by 12.7% in average success rate. Further evaluation on six representative tasks demonstrates strong zero-shot view generalization, with success rate drops of only 22.0% and 29.7% under moderate and large viewpoint shifts respectively, whereas the state-of-the-art method suffers larger decreases of 41.6% and 51.5%.

We introduce Cosmos, a framework for object-centric world modeling that is designed for compositional generalization (CG), i.e., high performance on unseen input scenes obtained through the composition of known visual "atoms." The central insight behind Cosmos is the use of a novel form of neurosymbolic grounding. Specifically, the framework introduces two new tools: (i) neurosymbolic scene encodings, which represent each entity in a scene using a real vector computed using a neural encoder, as well as a vector of composable symbols describing attributes of the entity, and (ii) a neurosymbolic attention mechanism that binds these entities to learned rules of interaction. Cosmos is end-to-end differentiable; also, unlike traditional neurosymbolic methods that require representations to be manually mapped to symbols, it computes an entity's symbolic attributes using vision-language foundation models. Through an evaluation that considers two different forms of CG on an established blocks-pushing domain, we show that the framework establishes a new state-of-the-art for CG in world modeling.

Learning good representations is essential for latent planning with world models. While pretrained visual encoders produce strong semantic visual features, they are not tailored to planning and contain information irrelevant -- or even detrimental -- to planning. Inspired by the perceptual straightening hypothesis in human visual processing, we introduce temporal straightening to improve representation learning for latent planning. Using a curvature regularizer that encourages locally straightened latent trajectories, we jointly learn an encoder and a predictor. We show that reducing curvature this way makes the Euclidean distance in latent space a better proxy for the geodesic distance and improves the conditioning of the planning objective. We demonstrate empirically that temporal straightening makes gradient-based planning more stable and yields significantly higher success rates across a suite of goal-reaching tasks.

Grounding language to the visual observations of a navigating agent can be performed using off-the-shelf visual-language models pretrained on Internet-scale data (e.g., image captions). While this is useful for matching images to natural language descriptions of object goals, it remains disjoint from the process of mapping the environment, so that it lacks the spatial precision of classic geometric maps. To address this problem, we propose VLMaps, a spatial map representation that directly fuses pretrained visual-language features with a 3D reconstruction of the physical world. VLMaps can be autonomously built from video feed on robots using standard exploration approaches and enables natural language indexing of the map without additional labeled data. Specifically, when combined with large language models (LLMs), VLMaps can be used to (i) translate natural language commands into a sequence of open-vocabulary navigation goals (which, beyond prior work, can be spatial by construction, e.g., "in between the sofa and TV" or "three meters to the right of the chair") directly localized in the map, and (ii) can be shared among multiple robots with different embodiments to generate new obstacle maps on-the-fly (by using a list of obstacle categories). Extensive experiments carried out in simulated and real world environments show that VLMaps enable navigation according to more complex language instructions than existing methods. Videos are available at https://vlmaps.github.io.

Recent advances in video world modeling have enabled large-scale generative models to simulate embodied environments with high visual fidelity, providing strong priors for prediction, planning, and control. Yet, despite their realism, these models often lack geometric grounding, limiting their use in navigation tasks that require spatial coherence and long-horizon stability. We introduce Reinforcement Learning with World Grounding (RLWG), a self-supervised post-training framework that aligns pretrained world models with a physically verifiable structure through geometric and perceptual rewards. Analogous to reinforcement learning from verifiable feedback (RLVR) in language models, RLWG can use multiple rewards that measure pose cycle-consistency, depth reprojection, and temporal coherence. We instantiate this framework with GrndCtrl, a reward-aligned adaptation method based on Group Relative Policy Optimization (GRPO), yielding world models that maintain stable trajectories, consistent geometry, and reliable rollouts for embodied navigation. Like post-training alignment in large language models, GrndCtrl leverages verifiable rewards to bridge generative pretraining and grounded behavior, achieving superior spatial coherence and navigation stability over supervised fine-tuning in outdoor environments.

In this paper, we question whether we have a reliable self-supervised point cloud model that can be used for diverse 3D tasks via simple linear probing, even with limited data and minimal computation. We find that existing 3D self-supervised learning approaches fall short when evaluated on representation quality through linear probing. We hypothesize that this is due to what we term the "geometric shortcut", which causes representations to collapse to low-level spatial features. This challenge is unique to 3D and arises from the sparse nature of point cloud data. We address it through two key strategies: obscuring spatial information and enhancing the reliance on input features, ultimately composing a Sonata of 140k point clouds through self-distillation. Sonata is simple and intuitive, yet its learned representations are strong and reliable: zero-shot visualizations demonstrate semantic grouping, alongside strong spatial reasoning through nearest-neighbor relationships. Sonata demonstrates exceptional parameter and data efficiency, tripling linear probing accuracy (from 21.8% to 72.5%) on ScanNet and nearly doubling performance with only 1% of the data compared to previous approaches. Full fine-tuning further advances SOTA across both 3D indoor and outdoor perception tasks.

Scene generation with 3D assets presents a complex challenge, requiring both high-level semantic understanding and low-level geometric reasoning. While Multimodal Large Language Models (MLLMs) excel at semantic tasks, their application to 3D scene generation is hindered by their limited grounding on 3D geometry. In this paper, we investigate how to best work with MLLMs in an object placement task. Towards this goal, we introduce a novel framework, FirePlace, that applies existing MLLMs in (1) 3D geometric reasoning and the extraction of relevant geometric details from the 3D scene, (2) constructing and solving geometric constraints on the extracted low-level geometry, and (3) pruning for final placements that conform to common sense. By combining geometric reasoning with real-world understanding of MLLMs, our method can propose object placements that satisfy both geometric constraints as well as high-level semantic common-sense considerations. Our experiments show that these capabilities allow our method to place objects more effectively in complex scenes with intricate geometry, surpassing the quality of prior work.

Semantic navigation requires an agent to navigate toward a specified target in an unseen environment. Employing an imaginative navigation strategy that predicts future scenes before taking action, can empower the agent to find target faster. Inspired by this idea, we propose SGImagineNav, a novel imaginative navigation framework that leverages symbolic world modeling to proactively build a global environmental representation. SGImagineNav maintains an evolving hierarchical scene graphs and uses large language models to predict and explore unseen parts of the environment. While existing methods solely relying on past observations, this imaginative scene graph provides richer semantic context, enabling the agent to proactively estimate target locations. Building upon this, SGImagineNav adopts an adaptive navigation strategy that exploits semantic shortcuts when promising and explores unknown areas otherwise to gather additional context. This strategy continuously expands the known environment and accumulates valuable semantic contexts, ultimately guiding the agent toward the target. SGImagineNav is evaluated in both real-world scenarios and simulation benchmarks. SGImagineNav consistently outperforms previous methods, improving success rate to 65.4 and 66.8 on HM3D and HSSD, and demonstrating cross-floor and cross-room navigation in real-world environments, underscoring its effectiveness and generalizability.

In this paper, we claim that 3D visual grounding is the cornerstone of spatial reasoning and introduce the Grounded-Spatial Reasoner (GS-Reasoner) to explore the effective spatial representations that bridge the gap between them. Existing 3D LLMs suffer from the absence of a unified 3D representation capable of jointly capturing semantic and geometric information. This deficiency is manifested either in poor performance on grounding or in an excessive reliance on external modules, ultimately hindering the seamless integration of grounding and spatial reasoning. To address this, we propose a simple yet effective dual-path pooling mechanism that tightly aligns geometric features with both semantic and positional cues, constructing a unified image patch-based 3D representation that encapsulates all essential information without increasing the number of input tokens. Leveraging this holistic representation, GS-Reasoner is the first 3D LLM that achieves autoregressive grounding entirely without external modules while delivering performance comparable to state-of-the-art models, establishing a unified and self-contained framework for 3D spatial reasoning. To further bridge grounding and spatial reasoning, we introduce the Grounded Chain-of-Thought (GCoT) dataset. This dataset is meticulously curated to include both 3D bounding box annotations for objects referenced in reasoning questions and step-by-step reasoning paths that integrate grounding as a core component of the problem-solving process. Extensive experiments demonstrate that GS-Reasoner achieves impressive results on 3D visual grounding, which in turn significantly enhances its spatial reasoning capabilities, leading to state-of-the-art performance.

Humans construct internal world models and reason by manipulating the concepts within these models. Recent advances in AI, particularly chain-of-thought (CoT) reasoning, approximate such human cognitive abilities, where world models are believed to be embedded within large language models. Expert-level performance in formal and abstract domains such as mathematics and programming has been achieved in current systems by relying predominantly on verbal reasoning. However, they still lag far behind humans in domains like physical and spatial intelligence, which require richer representations and prior knowledge. The emergence of unified multimodal models (UMMs) capable of both verbal and visual generation has therefore sparked interest in more human-like reasoning grounded in complementary multimodal pathways, though their benefits remain unclear. From a world-model perspective, this paper presents the first principled study of when and how visual generation benefits reasoning. Our key position is the visual superiority hypothesis: for certain tasks--particularly those grounded in the physical world--visual generation more naturally serves as world models, whereas purely verbal world models encounter bottlenecks arising from representational limitations or insufficient prior knowledge. Theoretically, we formalize internal world modeling as a core component of CoT reasoning and analyze distinctions among different forms of world models. Empirically, we identify tasks that necessitate interleaved visual-verbal CoT reasoning, constructing a new evaluation suite, VisWorld-Eval. Controlled experiments on a state-of-the-art UMM show that interleaved CoT significantly outperforms purely verbal CoT on tasks that favor visual world modeling, but offers no clear advantage otherwise. Together, this work clarifies the potential of multimodal world modeling for more powerful, human-like multimodal AI.

This paper presents GPSM4K, a comprehensive geometry multimodal dataset tailored to augment the problem-solving capabilities of Large Vision Language Models (LVLMs). GPSM4K encompasses 2157 multimodal question-answer pairs manually extracted from mathematics textbooks spanning grades 7-12 and is further augmented to 5340 problems, consisting of both numerical and theorem-proving questions. In contrast to PGPS9k, Geometry3K, and Geo170K which feature only objective-type questions, GPSM4K offers detailed step-by-step solutions in a consistent format, facilitating a comprehensive evaluation of problem-solving approaches. This dataset serves as an excellent benchmark for assessing the geometric reasoning capabilities of LVLMs. Evaluation of our test set shows that there is scope for improvement needed in open-source language models in geometry problem-solving. Finetuning on our training set increases the geometry problem-solving capabilities of models. Further, We also evaluate the effectiveness of techniques such as image captioning and Retrieval Augmentation generation (RAG) on model performance. We leveraged LLM to automate the task of final answer evaluation by providing ground truth and predicted solutions. This research will help to assess and improve the geometric reasoning capabilities of LVLMs.

Explorable 3D world generation from a single image or text prompt forms a cornerstone of spatial intelligence. Recent works utilize video model to achieve wide-scope and generalizable 3D world generation. However, existing approaches often suffer from a limited scope in the generated scenes. In this work, we propose Matrix-3D, a framework that utilize panoramic representation for wide-coverage omnidirectional explorable 3D world generation that combines conditional video generation and panoramic 3D reconstruction. We first train a trajectory-guided panoramic video diffusion model that employs scene mesh renders as condition, to enable high-quality and geometrically consistent scene video generation. To lift the panorama scene video to 3D world, we propose two separate methods: (1) a feed-forward large panorama reconstruction model for rapid 3D scene reconstruction and (2) an optimization-based pipeline for accurate and detailed 3D scene reconstruction. To facilitate effective training, we also introduce the Matrix-Pano dataset, the first large-scale synthetic collection comprising 116K high-quality static panoramic video sequences with depth and trajectory annotations. Extensive experiments demonstrate that our proposed framework achieves state-of-the-art performance in panoramic video generation and 3D world generation. See more in https://matrix-3d.github.io.

Scene-level 3D generation is a challenging research topic, with most existing methods generating only partial scenes and offering limited navigational freedom. We introduce WorldPrompter, a novel generative pipeline for synthesizing traversable 3D scenes from text prompts. We leverage panoramic videos as an intermediate representation to model the 360{\deg} details of a scene. WorldPrompter incorporates a conditional 360{\deg} panoramic video generator, capable of producing a 128-frame video that simulates a person walking through and capturing a virtual environment. The resulting video is then reconstructed as Gaussian splats by a fast feedforward 3D reconstructor, enabling a true walkable experience within the 3D scene. Experiments demonstrate that our panoramic video generation model achieves convincing view consistency across frames, enabling high-quality panoramic Gaussian splat reconstruction and facilitating traversal over an area of the scene. Qualitative and quantitative results also show it outperforms the state-of-the-art 360{\deg} video generators and 3D scene generation models.

Plane geometry problem solving (PGPS) has recently gained significant attention as a benchmark to assess the multi-modal reasoning capabilities of large vision-language models. Despite the growing interest in PGPS, the research community still lacks a comprehensive overview that systematically synthesizes recent work in PGPS. To fill this gap, we present a survey of existing PGPS studies. We first categorize PGPS methods into an encoder-decoder framework and summarize the corresponding output formats used by their encoders and decoders. Subsequently, we classify and analyze these encoders and decoders according to their architectural designs. Finally, we outline major challenges and promising directions for future research. In particular, we discuss the hallucination issues arising during the encoding phase within encoder-decoder architectures, as well as the problem of data leakage in current PGPS benchmarks.

Since a building's floorplans are easily accessible, consistent over time, and inherently robust to changes in visual appearance, self-localization within the floorplan has attracted researchers' interest. However, since floorplans are minimalist representations of a building's structure, modal and geometric differences between visual perceptions and floorplans pose challenges to this task. While existing methods cleverly utilize 2D geometric features and pose filters to achieve promising performance, they fail to address the localization errors caused by frequent visual changes and view occlusions due to variously shaped 3D objects. To tackle these issues, this paper views the 2D Floorplan Localization (FLoc) problem from a higher dimension by injecting 3D geometric priors into the visual FLoc algorithm. For the 3D geometric prior modeling, we first model geometrically aware view invariance using multi-view constraints, i.e., leveraging imaging geometric principles to provide matching constraints between multiple images that see the same points. Then, we further model the view-scene aligned geometric priors, enhancing the cross-modal geometry-color correspondences by associating the scene's surface reconstruction with the RGB frames of the sequence. Both 3D priors are modeled through self-supervised contrastive learning, thus no additional geometric or semantic annotations are required. These 3D priors summarized in extensive realistic scenes bridge the modal gap while improving localization success without increasing the computational burden on the FLoc algorithm. Sufficient comparative studies demonstrate that our method significantly outperforms state-of-the-art methods and substantially boosts the FLoc accuracy. All data and code will be released after the anonymous review.

We introduce the Reality-linked 3D Scenes (R3DS) dataset of synthetic 3D scenes mirroring the real-world scene arrangements from Matterport3D panoramas. Compared to prior work, R3DS has more complete and densely populated scenes with objects linked to real-world observations in panoramas. R3DS also provides an object support hierarchy, and matching object sets (e.g., same chairs around a dining table) for each scene. Overall, R3DS contains 19K objects represented by 3,784 distinct CAD models from over 100 object categories. We demonstrate the effectiveness of R3DS on the Panoramic Scene Understanding task. We find that: 1) training on R3DS enables better generalization; 2) support relation prediction trained with R3DS improves performance compared to heuristically calculated support; and 3) R3DS offers a challenging benchmark for future work on panoramic scene understanding.

Existing fully-supervised point cloud segmentation methods suffer in the dynamic testing environment with emerging new classes. Few-shot point cloud segmentation algorithms address this problem by learning to adapt to new classes at the sacrifice of segmentation accuracy for the base classes, which severely impedes its practicality. This largely motivates us to present the first attempt at a more practical paradigm of generalized few-shot point cloud segmentation, which requires the model to generalize to new categories with only a few support point clouds and simultaneously retain the capability to segment base classes. We propose the geometric words to represent geometric components shared between the base and novel classes, and incorporate them into a novel geometric-aware semantic representation to facilitate better generalization to the new classes without forgetting the old ones. Moreover, we introduce geometric prototypes to guide the segmentation with geometric prior knowledge. Extensive experiments on S3DIS and ScanNet consistently illustrate the superior performance of our method over baseline methods. Our code is available at: https://github.com/Pixie8888/GFS-3DSeg_GWs.

World models have garnered significant attention as a promising research direction in artificial intelligence, yet a clear and unified definition remains lacking. In this paper, we introduce OpenWorldLib, a comprehensive and standardized inference framework for Advanced World Models. Drawing on the evolution of world models, we propose a clear definition: a world model is a model or framework centered on perception, equipped with interaction and long-term memory capabilities, for understanding and predicting the complex world. We further systematically categorize the essential capabilities of world models. Based on this definition, OpenWorldLib integrates models across different tasks within a unified framework, enabling efficient reuse and collaborative inference. Finally, we present additional reflections and analyses on potential future directions for world model research. Code link: https://github.com/OpenDCAI/OpenWorldLib

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k.

World models that forecast scene evolution by generating future video frames devote the bulk of their capacity to photometric details, yet the resulting predictions often remain geometrically inconsistent. We present VGGT-World, a geometry world model that side-steps video generation entirely and instead forecasts the temporal evolution of frozen geometry-foundation-model (GFM) features. Concretely, we repurpose the latent tokens of a frozen VGGT as the world state and train a lightweight temporal flow transformer to autoregressively predict their future trajectory. Two technical challenges arise in this high-dimensional (d=1024) feature space: (i) standard velocity-prediction flow matching collapses, and (ii) autoregressive rollout suffers from compounding exposure bias. We address the first with a clean-target (z-prediction) parameterization that yields a substantially higher signal-to-noise ratio, and the second with a two-stage latent flow-forcing curriculum that progressively conditions the model on its own partially denoised rollouts. Experiments on KITTI, Cityscapes, and TartanAir demonstrate that VGGT-World significantly outperforms the strongest baselines in depth forecasting while running 3.6-5 times faster with only 0.43B trainable parameters, establishing frozen GFM features as an effective and efficient predictive state for 3D world modeling.

Despite recent advances in multimodal content generation enabled by vision-language models (VLMs), their ability to reason about and generate structured 3D scenes remains largely underexplored. This limitation constrains their utility in spatially grounded tasks such as embodied AI, immersive simulations, and interactive 3D applications. We introduce a new paradigm that enables VLMs to generate, understand, and edit complex 3D environments by injecting a continually evolving spatial context. Constructed from multimodal input, this context consists of three components: a scene portrait that provides a high-level semantic blueprint, a semantically labeled point cloud capturing object-level geometry, and a scene hypergraph that encodes rich spatial relationships, including unary, binary, and higher-order constraints. Together, these components provide the VLM with a structured, geometry-aware working memory that integrates its inherent multimodal reasoning capabilities with structured 3D understanding for effective spatial reasoning. Building on this foundation, we develop an agentic 3D scene generation pipeline in which the VLM iteratively reads from and updates the spatial context. The pipeline features high-quality asset generation with geometric restoration, environment setup with automatic verification, and ergonomic adjustment guided by the scene hypergraph. Experiments show that our framework can handle diverse and challenging inputs, achieving a level of generalization not observed in prior work. Further results demonstrate that injecting spatial context enables VLMs to perform downstream tasks such as interactive scene editing and path planning, suggesting strong potential for spatially intelligent systems in computer graphics, 3D vision, and embodied applications.

Vision-language models (VLM) excel at general understanding yet remain weak at dynamic spatial reasoning (DSR), i.e., reasoning about the evolvement of object geometry and relationship in 3D space over time, largely due to the scarcity of scalable 4D-aware training resources. To bridge this gap across aspects of dataset, benchmark and model, we introduce DSR Suite. First, we propose an automated pipeline that generates multiple-choice question-answer pairs from in-the-wild videos for DSR. By leveraging modern vision foundation models, the pipeline extracts rich geometric and motion information, including camera poses, local point clouds, object masks, orientations, and 3D trajectories. These geometric cues enable the construction of DSR-Train for learning and further human-refined DSR-Bench for evaluation. Compared with previous works, our data emphasize (i) in-the-wild video sources, (ii) object- and scene-level 3D requirements, (iii) viewpoint transformations, (iv) multi-object interactions, and (v) fine-grained, procedural answers. Beyond data, we propose a lightweight Geometry Selection Module (GSM) to seamlessly integrate geometric priors into VLMs, which condenses question semantics and extracts question-relevant knowledge from pretrained 4D reconstruction priors into a compact set of geometry tokens. This targeted extraction avoids overwhelming the model with irrelevant knowledge. Experiments show that integrating DSR-Train and GSM into Qwen2.5-VL-7B significantly enhances its dynamic spatial reasoning capability, while maintaining accuracy on general video understanding benchmarks.

3D scene graphs have recently emerged as a powerful high-level representation of 3D environments. A 3D scene graph describes the environment as a layered graph where nodes represent spatial concepts at multiple levels of abstraction and edges represent relations between concepts. While 3D scene graphs can serve as an advanced "mental model" for robots, how to build such a rich representation in real-time is still uncharted territory. This paper describes a real-time Spatial Perception System, a suite of algorithms to build a 3D scene graph from sensor data in real-time. Our first contribution is to develop real-time algorithms to incrementally construct the layers of a scene graph as the robot explores the environment; these algorithms build a local Euclidean Signed Distance Function (ESDF) around the current robot location, extract a topological map of places from the ESDF, and then segment the places into rooms using an approach inspired by community-detection techniques. Our second contribution is to investigate loop closure detection and optimization in 3D scene graphs. We show that 3D scene graphs allow defining hierarchical descriptors for loop closure detection; our descriptors capture statistics across layers in the scene graph, ranging from low-level visual appearance to summary statistics about objects and places. We then propose the first algorithm to optimize a 3D scene graph in response to loop closures; our approach relies on embedded deformation graphs to simultaneously correct all layers of the scene graph. We implement the proposed Spatial Perception System into a architecture named Hydra, that combines fast early and mid-level perception processes with slower high-level perception. We evaluate Hydra on simulated and real data and show it is able to reconstruct 3D scene graphs with an accuracy comparable with batch offline methods despite running online.

Large-scale pre-training has shown promising results on the vision-and-language navigation (VLN) task. However, most existing pre-training methods employ discrete panoramas to learn visual-textual associations. This requires the model to implicitly correlate incomplete, duplicate observations within the panoramas, which may impair an agent's spatial understanding. Thus, we propose a new map-based pre-training paradigm that is spatial-aware for use in VLN. Concretely, we build a local metric map to explicitly aggregate incomplete observations and remove duplicates, while modeling navigation dependency in a global topological map. This hybrid design can balance the demand of VLN for both short-term reasoning and long-term planning. Then, based on the hybrid map, we devise a pre-training framework to learn a multimodal map representation, which enhances spatial-aware cross-modal reasoning thereby facilitating the language-guided navigation goal. Extensive experiments demonstrate the effectiveness of the map-based pre-training route for VLN, and the proposed method achieves state-of-the-art on four VLN benchmarks.

Effective robotic manipulation relies on a precise understanding of 3D scene geometry, and one of the most straightforward ways to acquire such geometry is through multi-view observations. Motivated by this, we present GP3 -- a 3D geometry-aware robotic manipulation policy that leverages multi-view input. GP3 employs a spatial encoder to infer dense spatial features from RGB observations, which enable the estimation of depth and camera parameters, leading to a compact yet expressive 3D scene representation tailored for manipulation. This representation is fused with language instructions and translated into continuous actions via a lightweight policy head. Comprehensive experiments demonstrate that GP3 consistently outperforms state-of-the-art methods on simulated benchmarks. Furthermore, GP3 transfers effectively to real-world robots without depth sensors or pre-mapped environments, requiring only minimal fine-tuning. These results highlight GP3 as a practical, sensor-agnostic solution for geometry-aware robotic manipulation.

Recent advancements in Spatial Intelligence (SI) have predominantly relied on Vision-Language Models (VLMs), yet a critical question remains: does spatial understanding originate from visual encoders or the fundamental reasoning backbone? Inspired by this question, we introduce SiT-Bench, a novel benchmark designed to evaluate the SI performance of Large Language Models (LLMs) without pixel-level input, comprises over 3,800 expert-annotated items across five primary categories and 17 subtasks, ranging from egocentric navigation and perspective transformation to fine-grained robotic manipulation. By converting single/multi-view scenes into high-fidelity, coordinate-aware textual descriptions, we challenge LLMs to perform symbolic textual reasoning rather than visual pattern matching. Evaluation results of state-of-the-art (SOTA) LLMs reveals that while models achieve proficiency in localized semantic tasks, a significant "spatial gap" remains in global consistency. Notably, we find that explicit spatial reasoning significantly boosts performance, suggesting that LLMs possess latent world-modeling potential. Our proposed dataset SiT-Bench serves as a foundational resource to foster the development of spatially-grounded LLM backbones for future VLMs and embodied agents. Our code and benchmark will be released at https://github.com/binisalegend/SiT-Bench .

Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities, which encourages extensive research on their application in mathematical problem solving. However, current work has been largely focused on text-based mathematical problems, with limited investigation in problems involving geometric information. Addressing this gap, we aim to enable LLMs to solve geometric problems by understanding image input. We first analyze the limitations of current Multimodal Large Language Models (MLLMs) in this area: they struggle to accurately comprehending basic geometric elements and their relationships. To overcome these challenges, we take advantage of the unique characteristics of geometric problems (such as unique geometric logical form, and geometric scalability) and the capacity of the textual LLMs to build an enriched multimodal geometry dataset based on existing data. The augmented dataset, Geo170K, contains more than 170K geometric image-caption and question-answer pairs. Utilizing our constructed Geo170K dataset, we develop G-LLaVA, which demonstrates exceptional performance in solving geometric problems, significantly outperforming GPT-4-V on the MathVista benchmark with only 7B parameters.

Vision-language models (VLMs) often struggle with geometric reasoning due to their limited perception of fundamental diagram elements. To tackle this challenge, we introduce GeoPerceive, a benchmark comprising diagram instances paired with domain-specific language (DSL) representations, along with an efficient automatic data generation pipeline. This design enables the isolated evaluation of geometric perception independently from reasoning. To exploit the data provided by GeoPerceive for enhancing the geometric perception capabilities of VLMs, we propose GeoDPO, a translator-guided reinforcement learning (RL) framework. GeoDPO employs an NL-to-DSL translator, which is trained on synthetic pairs generated by the data engine of GeoPerceive, to bridge natural language and DSL. This translator facilitates the computation of fine-grained, DSL-level scores, which serve as reward signals in reinforcement learning. We assess GeoDPO on both in-domain and out-of-domain datasets, spanning tasks in geometric perception as well as downstream reasoning. Experimental results demonstrate that, while supervised fine-tuning (SFT) offers only marginal improvements and may even impair performance in out-of-domain scenarios, GeoDPO achieves substantial gains: +26.5% on in-domain data, +8.0% on out-of-domain data, and +39.0% on downstream reasoning tasks. These findings underscore the superior performance and generalization ability of GeoDPO over SFT. All codes are released at https://github.com/Longin-Yu/GeoPerceive to ensure reproducibility.

Given a set of calibrated images of a scene, we present an approach that produces a simple, compact, and actionable 3D world representation by means of 3D primitives. While many approaches focus on recovering high-fidelity 3D scenes, we focus on parsing a scene into mid-level 3D representations made of a small set of textured primitives. Such representations are interpretable, easy to manipulate and suited for physics-based simulations. Moreover, unlike existing primitive decomposition methods that rely on 3D input data, our approach operates directly on images through differentiable rendering. Specifically, we model primitives as textured superquadric meshes and optimize their parameters from scratch with an image rendering loss. We highlight the importance of modeling transparency for each primitive, which is critical for optimization and also enables handling varying numbers of primitives. We show that the resulting textured primitives faithfully reconstruct the input images and accurately model the visible 3D points, while providing amodal shape completions of unseen object regions. We compare our approach to the state of the art on diverse scenes from DTU, and demonstrate its robustness on real-life captures from BlendedMVS and Nerfstudio. We also showcase how our results can be used to effortlessly edit a scene or perform physical simulations. Code and video results are available at https://www.tmonnier.com/DBW .

Mapping is crucial for spatial reasoning, planning and robot navigation. Existing approaches range from metric, which require precise geometry-based optimization, to purely topological, where image-as-node based graphs lack explicit object-level reasoning and interconnectivity. In this paper, we propose a novel topological representation of an environment based on "image segments", which are semantically meaningful and open-vocabulary queryable, conferring several advantages over previous works based on pixel-level features. Unlike 3D scene graphs, we create a purely topological graph with segments as nodes, where edges are formed by a) associating segment-level descriptors between pairs of consecutive images and b) connecting neighboring segments within an image using their pixel centroids. This unveils a "continuous sense of a place", defined by inter-image persistence of segments along with their intra-image neighbours. It further enables us to represent and update segment-level descriptors through neighborhood aggregation using graph convolution layers, which improves robot localization based on segment-level retrieval. Using real-world data, we show how our proposed map representation can be used to i) generate navigation plans in the form of "hops over segments" and ii) search for target objects using natural language queries describing spatial relations of objects. Furthermore, we quantitatively analyze data association at the segment level, which underpins inter-image connectivity during mapping and segment-level localization when revisiting the same place. Finally, we show preliminary trials on segment-level `hopping' based zero-shot real-world navigation. Project page with supplementary details: oravus.github.io/RoboHop/

We present Spatial Region 3D (SR-3D) aware vision-language model that connects single-view 2D images and multi-view 3D data through a shared visual token space. SR-3D supports flexible region prompting, allowing users to annotate regions with bounding boxes, segmentation masks on any frame, or directly in 3D, without the need for exhaustive multi-frame labeling. We achieve this by enriching 2D visual features with 3D positional embeddings, which allows the 3D model to draw upon strong 2D priors for more accurate spatial reasoning across frames, even when objects of interest do not co-occur within the same view. Extensive experiments on both general 2D vision language and specialized 3D spatial benchmarks demonstrate that SR-3D achieves state-of-the-art performance, underscoring its effectiveness for unifying 2D and 3D representation space on scene understanding. Moreover, we observe applicability to in-the-wild videos without sensory 3D inputs or ground-truth 3D annotations, where SR-3D accurately infers spatial relationships and metric measurements.

Recent advancements in reinforcement learning (RL) have enhanced the reasoning abilities of large language models (LLMs), yet the impact on multimodal LLMs (MLLMs) is limited. Particularly in vision-intensive tasks like geometric reasoning, MLLMs hallucinate frequently, leading to inaccurate reasoning. We attribute this to the perceptual bottleneck in MLLMs, which caps the benefits of reasoning training. To quantify this, we design a Geo-Perception Question-Answering (GeoPQA) benchmark, targeting basic geometric concepts and spatial relationships. Experiments on GeoPQA reveal significant shortcomings of MLLMs in visual perception, which constrain RL reward signals for effective training. To address this bottleneck, we propose a two-stage RL training framework by first enhancing the visual perception of geometric structures, then fostering reasoning capabilities. Applied to Qwen2.5-VL-3B-Instruct, our two-stage training improves geometric reasoning by 9.7% and geometric problem solving by 9.1%, compared to the direct reasoning training approach. Our method also generalizes to other vision-intensive domains like figure understanding, highlighting the importance of perceptual grounding in effective MLLM reasoning.

This is not a typical survey of world models; it is a guide for those who want to build worlds. We do not aim to catalog every paper that has ever mentioned a ``world model". Instead, we follow one clear road: from early masked models that unified representation learning across modalities, to unified architectures that share a single paradigm, then to interactive generative models that close the action-perception loop, and finally to memory-augmented systems that sustain consistent worlds over time. We bypass loosely related branches to focus on the core: the generative heart, the interactive loop, and the memory system. We show that this is the most promising path towards true world models.

Panorama images have a much larger field-of-view thus naturally encode enriched scene context information compared to standard perspective images, which however is not well exploited in the previous scene understanding methods. In this paper, we propose a novel method for panoramic 3D scene understanding which recovers the 3D room layout and the shape, pose, position, and semantic category for each object from a single full-view panorama image. In order to fully utilize the rich context information, we design a novel graph neural network based context model to predict the relationship among objects and room layout, and a differentiable relationship-based optimization module to optimize object arrangement with well-designed objective functions on-the-fly. Realizing the existing data are either with incomplete ground truth or overly-simplified scene, we present a new synthetic dataset with good diversity in room layout and furniture placement, and realistic image quality for total panoramic 3D scene understanding. Experiments demonstrate that our method outperforms existing methods on panoramic scene understanding in terms of both geometry accuracy and object arrangement. Code is available at https://chengzhag.github.io/publication/dpc.

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic and spherical spaces show promise for hierarchical and cyclical patterns, respectively, they require committing to a single geometry a priori, reducing flexibility when data exhibits mixed geometric properties. We introduce the Curvature-Adaptive Transformer (CAT), a novel architecture that dynamically learns per-token routing across three geometric attention branches through a lightweight, differentiable gating mechanism. Unlike fixed-geometry approaches, CAT enables adaptive geometric specialization, routing tokens to the appropriate curvature based on their local relational structure. The routing network provides interpretable curvature preferences while each branch employs geometry-specific operations optimized for its respective manifold. On knowledge graph completion benchmarks (FB15k-237, WN18RR), CAT achieves approximately 10% improvements in MRR and Hits@10 over fixed-geometry baselines with minimal overhead (5% parameter increase, comparable inference time). These results demonstrate that learned geometric adaptation outperforms any single fixed geometry for complex relational reasoning, establishing CAT as a scalable and interpretable foundation for mixture-of-geometry architectures across language, vision, and multimodal domains.

Geometric diagrams are critical in conveying mathematical and scientific concepts, yet traditional diagram generation methods are often manual and resource-intensive. While text-to-image generation has made strides in photorealistic imagery, creating accurate geometric diagrams remains a challenge due to the need for precise spatial relationships and the scarcity of geometry-specific datasets. This paper presents MagicGeo, a training-free framework for generating geometric diagrams from textual descriptions. MagicGeo formulates the diagram generation process as a coordinate optimization problem, ensuring geometric correctness through a formal language solver, and then employs coordinate-aware generation. The framework leverages the strong language translation capability of large language models, while formal mathematical solving ensures geometric correctness. We further introduce MagicGeoBench, a benchmark dataset of 220 geometric diagram descriptions, and demonstrate that MagicGeo outperforms current methods in both qualitative and quantitative evaluations. This work provides a scalable, accurate solution for automated diagram generation, with significant implications for educational and academic applications.

Recent work in the construction of 3D scene graphs has enabled mobile robots to build large-scale metric-semantic hierarchical representations of the world. These detailed models contain information that is useful for planning, however an open question is how to derive a planning domain from a 3D scene graph that enables efficient computation of executable plans. In this work, we present a novel approach for defining and solving Task and Motion Planning problems in large-scale environments using hierarchical 3D scene graphs. We describe a method for building sparse problem instances which enables scaling planning to large scenes, and we propose a technique for incrementally adding objects to that domain during planning time that minimizes computation on irrelevant elements of the scene graph. We evaluate our approach in two real scene graphs built from perception, including one constructed from the KITTI dataset. Furthermore, we demonstrate our approach in the real world, building our representation, planning in it, and executing those plans on a real robotic mobile manipulator. A video supplement is available at https://youtu.be/v8fkwLjBn58.

Though recent advances in vision-language models (VLMs) have achieved remarkable progress across a wide range of multimodal tasks, understanding 3D spatial relationships from limited views remains a significant challenge. Previous reasoning methods typically rely on pure text (e.g., topological cognitive maps) or on 2D visual cues. However, their limited representational capacity hinders performance in specific tasks that require 3D spatial imagination. To address this limitation, we propose 3DThinker, a framework that can effectively exploits the rich geometric information embedded within images while reasoning, like humans do. Our framework is the first to enable 3D mentaling during reasoning without any 3D prior input, and it does not rely on explicitly labeled 3D data for training. Specifically, our training consists of two stages. First, we perform supervised training to align the 3D latent generated by VLM while reasoning with that of a 3D foundation model (e.g., VGGT). Then, we optimize the entire reasoning trajectory solely based on outcome signals, thereby refining the underlying 3D mentaling. Extensive experiments across multiple benchmarks show that 3DThinker consistently outperforms strong baselines and offers a new perspective toward unifying 3D representations into multimodal reasoning. Our code will be available at https://github.com/zhangquanchen/3DThinker.

Previous research has investigated the application of Multimodal Large Language Models (MLLMs) in understanding 3D scenes by interpreting them as videos. These approaches generally depend on comprehensive 3D data inputs, such as point clouds or reconstructed Bird's-Eye View (BEV) maps. In our research, we advance this field by enhancing the capability of MLLMs to understand and reason in 3D spaces directly from video data, without the need for additional 3D input. We propose a novel and efficient method, the Video-3D Geometry Large Language Model (VG LLM). Our approach employs a 3D visual geometry encoder that extracts 3D prior information from video sequences. This information is integrated with visual tokens and fed into the MLLM. Extensive experiments have shown that our method has achieved substantial improvements in various tasks related to 3D scene understanding and spatial reasoning, all directly learned from video sources. Impressively, our 4B model, which does not rely on explicit 3D data inputs, achieves competitive results compared to existing state-of-the-art methods, and even surpasses the Gemini-1.5-Pro in the VSI-Bench evaluations.

3D spatial understanding is essential in real-world applications such as robotics, autonomous vehicles, virtual reality, and medical imaging. Recently, Large Language Models (LLMs), having demonstrated remarkable success across various domains, have been leveraged to enhance 3D understanding tasks, showing potential to surpass traditional computer vision methods. In this survey, we present a comprehensive review of methods integrating LLMs with 3D spatial understanding. We propose a taxonomy that categorizes existing methods into three branches: image-based methods deriving 3D understanding from 2D visual data, point cloud-based methods working directly with 3D representations, and hybrid modality-based methods combining multiple data streams. We systematically review representative methods along these categories, covering data representations, architectural modifications, and training strategies that bridge textual and 3D modalities. Finally, we discuss current limitations, including dataset scarcity and computational challenges, while highlighting promising research directions in spatial perception, multi-modal fusion, and real-world applications.