Visual Spatial Reasoning

Image editing instructions are heterogeneous: a color swap, an object insertion, and a physical-action edit all demand different spatial coverage and different reasoning depth, yet existing reasoning-based editors apply a single fixed inference recipe to every instruction. We argue that adaptivity along both the spatial and temporal axes is the missing degree of freedom, and we present PhysEdit, an editing framework built around this principle. PhysEdit introduces two inference-time modules that compose without retraining the backbone. At its core, (1) Complexity-Adaptive Reasoning Depth (CARD) predicts edit complexity directly from the instruction and reference image and allocates the reasoning step count N_r and reasoning-token length r per sample -- turning a previously fixed inference schedule into a conditional-computation problem. CARD is supported by (2) a Spatial Reasoning Mask (SRM) that extracts an instruction-conditioned spatial prior from cross-attention to confine reasoning to regions that semantically require it. On the full 737-case ImgEdit Basic-Edit Suite, PhysEdit delivers a 1.18x wall-clock speedup (64.3s vs. 76.1s per sample) over a strong reasoning baseline while slightly improving instruction adherence (CLIP-T 0.2283 vs. 0.2266, +0.7%) and matching identity preservation within noise (CLIP-I 0.8246 vs. 0.8280). The speedup is category-dependent and reaches 1.52x on appearance-level edits, validating CARD's adaptive allocation as the principal source of efficiency gain. A 30-sample pilot with full ablations isolates the contribution of each module.

Vision-language models (VLMs) have shown strong performance on static visual understanding, yet they still struggle with dynamic spatial reasoning that requires imagining how scenes evolve under egocentric motion. Recent efforts address this limitation either by scaling spatial supervision with synthetic data or by coupling VLMs with world models at inference time. However, the former often lacks explicit modeling of motion-conditioned state transitions, while the latter incurs substantial computational overhead. In this work, we propose World2VLM, a training framework that distills spatial imagination from a generative world model into a vision-language model. Given an initial observation and a parameterized camera trajectory, we use a view-consistent world model to synthesize geometrically aligned future views and derive structured supervision for both forward (action-to-outcome) and inverse (outcome-to-action) spatial reasoning. We post-train the VLM with a two-stage recipe on a compact dataset generated by this pipeline and evaluate it on multiple spatial reasoning benchmarks. World2VLM delivers consistent improvements over the base model across diverse benchmarks, including SAT-Real, SAT-Synthesized, VSI-Bench, and MindCube. It also outperforms the test-time world-model-coupled methods while eliminating the need for expensive inference-time generation. Our results suggest that world models can serve not only as inference-time tools, but also as effective training-time teachers, enabling VLMs to internalize spatial imagination in a scalable and efficient manner.

Appreciating multi-figure paintings requires understanding how characters relate through subtle cues like gaze alignment, gesture, and spatial arrangement. We present MIRAGE, an evidence-centric framework designed to scaffold the exploration of these "micro-interactions" in multi-figure artworks. While such cues are essential for deep narrative appreciation, they are often distributed across complex scenes and difficult for viewers to systematically identify. Existing vision-language models (VLMs) frequently fail to provide reliable assistance, offering ungrounded interpretations that lack traceable visual evidence. MIRAGE addresses this by constructing a structured intermediate representation capturing identities, pose cues, and gaze hypotheses. However, the challenge extends beyond extracting these cues to coordinating them during interpretation. Without an explicit mechanism to organize and reconcile relational evidence, models often collapse multiple interaction hypotheses into a single unstable or weakly grounded narrative, even when low-level signals are available. This representation allows users to verify how high-level interpretations are anchored in low-level visual facts. By separating spatial grounding from narrative generation, MIRAGE enables users to inspect and reason about figure-to-figure relationships through a verifiable evidence layer. We evaluate MIRAGE against painting-only VLM baselines using a blind assessment protocol. Results show that MIRAGE significantly improves identity consistency, reduces relational hallucinations, and increases the coverage of subtle interactions. These findings suggest that structured grounding can serve as a critical interaction control layer, providing the necessary scaffolding for a more reliable, transparent, and human-led understanding of complex visual narratives.

Vision Transformers trained only on image classification routinely transfer to tasks that demand spatial understanding, yet they receive no spatial supervision during pretraining. We ask where and how robustly such structure is encoded. Probing a frozen ViT-B/16 layerwise for two complementary properties, local patch boundaries (BSDS500) and per-patch depth (NYU Depth V2), reveals a clear hierarchy: boundary structure becomes linearly decodable at layers 5-6 (AP = 0.833), while depth, which requires integrating global cues, peaks two to three layers later at layer 8 (MAE = 0.0875). Both signals collapse at the final classification layer, and random-weight controls confirm the encodings are learned rather than architectural. Causal interventions add specificity: ablating the single direction a linear depth probe reads degrades depth decoding by up to 165%, while ablating any other direction changes it by less than 1%. Targeted activation patching along that direction shows the depth signal is partially re-derived at each layer rather than passively carried in the residual stream, with mid-layer interventions persisting most strongly downstream. The result is that a classification-trained ViT develops an actively maintained spatial hierarchy that mirrors the early-to-late progression observed in the primate visual cortex.

Multimodal large language models (MLLMs) have advanced static visual--spatial reasoning, yet they often fail to preserve long-horizon spatial coherence in embodied settings where beliefs must be continuously revised from egocentric observations under environmental change. We introduce SpaMEM (Spatial Memory from Action Sequences), a large-scale diagnostic benchmark that isolates the mechanics of spatial belief evolution via action-conditioned scene transformations (spawn, place, remove) over long interaction horizons. SpaMEM is built on a physically grounded dataset with 10,601,392 high-fidelity images across four modalities (RGB, depth, instance, semantic segmentation), collected from 25,000+ interaction sequences in 1,000 procedurally generated houses. We formalize embodied spatial reasoning as a three-level hierarchy with 15 diagnostic tasks: Level 1 measures atomic spatial perception from single observations; Level 2 probes temporal reasoning with oracle textual state histories to factor out perceptual noise; and Level 3 requires end-to-end belief maintenance from raw visual streams under the same task dimensions. We further evaluate both short-term (step-wise) updates and long-term (episodic) reconstruction. Benchmarking representative open-source VLM families reveals a consistent stacked bottleneck: coordinate-consistent grounding remains a hard ceiling, and the sharp collapse from Level 2 to Level 3 exposes a pronounced symbolic scaffolding dependency, where models succeed with text-based bookkeeping but struggle to sustain robust visual memory. SpaMEM provides a granular diagnostic standard and motivates explicit mechanisms for state representation, belief revision, and long-horizon episodic integration. A subset of SpaMEM is publicly available at https://huggingface.co/datasets/mill-ct-liao/SpaMEM.

Visual planning represents a crucial facet of human intelligence, especially in tasks that require complex spatial reasoning and navigation. Yet, in machine learning, this inherently visual problem is often tackled through a verbal-centric lens. While recent research demonstrates the promise of fully visual approaches, they suffer from significant computational inefficiency due to the step-by-step planning-by-generation paradigm. In this work, we present EAR, an editing-as-reasoning paradigm that reformulates visual planning as a single-step image transformation. To isolate intrinsic reasoning from visual recognition, we employ abstract puzzles as probing tasks and introduce AMAZE, a procedurally generated dataset that features the classical Maze and Queen problems, covering distinct, complementary forms of visual planning. The abstract nature of AMAZE also facilitates automatic evaluation of autoregressive and diffusion-based models in terms of both pixel-wise fidelity and logical validity. We assess leading proprietary and open-source editing models. The results show that they all struggle in the zero-shot setting, finetuning on basic scales enables remarkable generalization to larger in-domain scales and out-of-domain scales and geometries. However, our best model that runs on high-end hardware fails to match the zero-shot efficiency of human solvers, highlighting a persistent gap in neural visual reasoning.

Understanding visual scenes requires not only recognizing objects but also reasoning about their spatial relationships. Unlike general vision-language tasks, spatial reasoning requires integrating multiple inductive biases, such as 2D appearance cues, depth signals, and geometric constraints, whose reliability varies across contexts. This suggests that effective spatial reasoning requires spatial adaptability: the ability to flexibly coordinate different reasoning strategies depending on the input. However, most existing approaches rely on a single reasoning pipeline that implicitly learns a fixed spatial prior, limiting their ability to adapt under distribution changes. Multi-agent systems offer a promising alternative by aggregating diverse reasoning trajectories, but prior attempts in spatial reasoning primarily employ homogeneous agents, restricting the diversity of inductive biases they can leverage. In this work, we introduce SpatiO, a heterogeneous multi-agent framework for spatial reasoning that coordinates multiple vision-language specialists with complementary inductive biases. To enable effective collaboration, we propose Test-Time Orchestration (TTO), an calibration mechanism that dynamically evaluates and reweights agents based on their observed reliability during inference, without modifying model parameters. Extensive experiments on diverse spatial reasoning benchmarks, including 3DSRBench, STVQA-7k, CV-Bench, and Omni3D-Bench, demonstrate that SpatiO consistently improves spatial reasoning performance over both closed-source and open-source baselines. The project page is available at https://cy-h1329.github.io/spatio/.

Spatial intelligence, which refers to the ability to reason about geometric and physical structure from visual observations, remains a core challenge for multimodal large language models. Despite promising performance, recent multimodal large language models (MLLMs) often exhibit fragile reasoning traces in spatial intelligence tasks that involve consistent spatial state recognition. We argue that these failures stem from a mismatch between the spatial recognition mechanism and the text-only reasoning behavior of these MLLMs. Effective spatial reasoning requires low-level geometric structure to be faithfully preserved and updated throughout the reasoning process, whereas textual representations tend to abstract away precisely these critical details. To address this issue, we propose SpatialImaginer, a unified multimodal generation framework that integrates textual reasoning with visual imagination. Our framework adopts a divide-and-conquer strategy, using text chain-of-thought for high-level semantic planning and the visual imagination for geometry-sensitive state transformation and consistency preservation. To support this capability, we further introduce a difficulty-aware data engine with closed-loop verification to train the model to invoke visual imagination selectively when stable spatial state tracking is required. Extensive experiments on diverse spatial intelligence benchmarks show that SpatialImaginer achieves state-of-the-art performance and substantially improves robustness on complex multi-step spatial reasoning tasks.

Implicit spatial relations and deep semantic structures encoded in object attributes are crucial for procedural planning in embodied AI systems. However, existing approaches often over rely on the reasoning capabilities of vision language models (VLMs) themselves, while overlooking the rich structured semantic information that can be mined from multimodal inputs. As a result, models struggle to effectively understand functional spatial relationships in complex scenes. To fully exploit implicit spatial relations and deep semantic structures in multimodal data, we propose GaLa, a vision language framework for multimodal procedural planning. GaLa introduces a hypergraph-based representation, where object instances in the image are modeled as nodes, and region-level hyperedges are constructed by aggregating objects according to their attributes and functional semantics. This design explicitly captures implicit semantic relations among objects as well as the hierarchical organization of functional regions. Furthermore, we design a TriView HyperGraph Encoder that enforces semantic consistency across the node view, area view, and node area association view via contrastive learning, enabling hypergraph semantics to be more effectively injected into downstream VLM reasoning. Extensive experiments on the ActPlan1K and ALFRED benchmarks demonstrate that GaLa significantly outperforms existing methods in terms of execution success rate, LCS, and planning correctness.

Multimodal Reasoning Models (MRMs) leveraging Chain-of-Thought (CoT) based thinking have revolutionized mathematical and logical problem-solving. However, we show that this paradigm struggles with generalized spatial intelligence. We perform a comprehensive evaluation of seventeen models across thirteen spatial benchmarks and identify a critical gap: CoT prompting consistently degrades performance in visual spatial reasoning. Furthermore, through a novel No-Image++ ablation, we demonstrate that MRMs and CoT prompted MLMs suffer from severe shortcut learning, and hallucinate visual details from textual priors even when the image is absent. These findings challenge the efficacy of text-only CoT for spatial tasks and underscore the need for vision-centric reasoning paradigms.

Multimodal large language models (MLLMs) have achieved impressive progress on vision language benchmarks, yet their capacity for visual cognitive and visuospatial reasoning remains less understood. We introduce "Mind's Eye", a multiple-choice benchmark of eight visuo-cognitive tasks inspired by classic human intelligence tests and organized under a novel "A-R-T" taxonomy: Abstraction, Relation, and Transformation. The tasks probe core processes of fluid intelligence such as pattern induction, analogical relation mapping, and mental transformation. We evaluate a diverse suite of closed-source and open-source MLLMs and compare their performance with human participants. Humans achieve 80% accuracy, while top performing MLLMs remain below 50%. Error analysis reveals failures in: (i) visual attention allocation, (ii) internal perceptual manipulation, and (iii) weak abstraction of underlying visual concepts. Our findings suggest that current MLLMs exhibit limited visuospatial reasoning capabilities, when compared with human participants, highlighting the need for more cognitively grounded evaluation frameworks.

Over the past year, spatial intelligence has drawn increasing attention. Many prior works study it from the perspective of visual-spatial intelligence, where models have access to visuospatial information from visual inputs. However, in the absence of visual information, whether linguistic intelligence alone is sufficient to endow models with spatial intelligence, and how models perform relevant tasks with text-only inputs still remain unexplored. Therefore, in this paper, we focus on a fundamental and critical capability in spatial intelligence from a linguistic perspective: viewpoint rotation understanding (VRU). Specifically, LLMs and VLMs are asked to infer their final viewpoint and predict the corresponding observation in an environment given textual description of viewpoint rotation and observation over multiple steps. We find that both LLMs and VLMs perform poorly on our proposed dataset while human can easily achieve 100% accuracy, indicating a substantial gap between current model capabilities and the requirements of spatial intelligence. To uncover the underlying mechanisms, we conduct a layer-wise probing analysis and head-wise causal intervention. Our findings reveal that although models encode viewpoint information in the hidden states, they appear to struggle to bind the viewpoint position with corresponding observation, resulting in a hallucination in final layers. Finally, we selectively fine-tune the key attention heads identified by causal intervention to improve VRU performance. Experimental results demonstrate that such selective fine-tuning achieves improved VRU performance while avoiding catastrophic forgetting of generic abilities. Our dataset and code will be released at https://github.com/Young-Zhen/VRU_Interpret .

GUI grounding models report over 85% accuracy on standard benchmarks, yet drop 27-56 percentage points when instructions require spatial reasoning rather than direct element naming. Current benchmarks miss this because they evaluate each screenshot once with a single fixed instruction. We introduce GUI-Perturbed, a controlled perturbation framework that independently varies visual scenes and instructions to measure grounding robustness. Evaluating three 7B models from the same architecture lineage, we find that relational instructions cause systematic accuracy collapse across all models, a 70% browser zoom produces statistically significant degradation, and rank-8 LoRA fine-tuning with augmented data degrades performance rather than improving it. By perturbing along independent axes, GUI-Perturbed isolates which specific capability axes are affected-spatial reasoning, visual robustness, reasoning calibration-providing diagnostic signal that aggregate benchmarks cannot. We release the dataset, augmentation pipeline, and a fine-tuned model.

Vision-language models (VLMs) still struggle with visual perception tasks such as spatial understanding and viewpoint recognition, largely because natural image datasets provide limited supervision for low-level visual skills. Can targeted synthetic supervision address these weaknesses without reference images or manual annotation? To investigate this, we introduce VisionFoundry, an automated pipeline that takes only a task name as input, uses LLMs to synthesize paired questions, answers, and text-to-image (T2I) prompts, generates images with T2I models, and filters samples via multimodal verification. With VisionFoundry, we construct VisionFoundry-10k, a synthetic VQA dataset spanning 10 perception tasks. Finetuning on VisionFoundry-10k consistently improves perception benchmarks across three open-source backbones (e.g., +6.7% on MMVP-pair and +10.5% on CV-Bench-3D for Qwen2.5-VL-3B-Instruct) while preserving broader capabilities and showing positive data scaling. The same synthetic supervision also yields consistent gains under reinforcement learning (RL) across all three backbones, and the framework remains effective under open-source synthesis and self-verification. Our findings demonstrate that automated synthetic supervision offers an effective and scalable path toward systematic VLM training.

Spatial reasoning is central to navigation and robotics, yet measuring model capabilities on these tasks remains difficult. Existing benchmarks evaluate models in a one-shot setting, requiring full solution generation in a single response, unlike humans, who work in interactive environments step-by-step. We introduce Spatial-Gym, a Gymnasium environment that isolates spatial constraint reasoning by testing pathfinding in 2D-grid puzzles as a sequential decision task with optional backtracking. We evaluate eight models in three settings (one-shot, step-by-step, step-by-step with backtracking) against human, random, and A* baselines on 500 episodes. The best model, GPT-OSS 120B, achieves a solve rate of 16.0%, 82 points below the human baseline (98.0%). Step-by-step format helps weaker models (up to +5.4%) by removing formatting errors, but hurts stronger models (up to 5.6%) by constraining global planning. Backtracking improves episode completion, but increases solve rate only for weaker models; stronger models rarely backtrack and do not benefit from it. Our experiments have three key findings: (1) models fail to scale reasoning effort with difficulty, (2) vision models receiving images of the spatial environment reduce solve rate by 73%, and (3) extended chain-of-thought reasoning retains a 3-5x accuracy advantage over standard inference even in the step-by-step setting. Spatial-Gym enables diagnosis of model limitations and provides a framework for improving spatial reasoning through reinforcement learning.

Reliable embodied interaction in indoor environments requires agents to precisely localize small everyday objects from visual observations. Yet this fundamental capability remains challenging for multimodal large language models (MLLMs), particularly when spatial understanding must be performed from indoor videos. Existing benchmarks study video spatial intelligence and embodied reasoning, but do not directly evaluate whether a model can localize a small target object and express its position with sufficient precision. We introduce PinpointQA, a benchmark built from ScanNet++ and ScanNet200. It contains 1,024 scenes and 10,094 QA pairs across four progressively challenging tasks: Target Presence Verification, Nearest Reference Identification, Fine-Grained Spatial Description, and Structured Spatial Prediction. Ground-truth annotations are constructed from intermediate spatial representations derived from aligned 3D geometry and instance-level annotations, while evaluated models receive only sampled RGB video frames. Evaluations of representative MLLMs reveal a consistent performance decline across the task progression, with structured spatial prediction remaining particularly challenging, while supervised fine-tuning substantially improves performance. By isolating the spatial grounding capabilities that precede downstream embodied interaction, PinpointQA serves as both a diagnostic benchmark and an effective training resource. The project page is available at https://rainchowz.github.io/PinpointQA/.

Multimodal reasoning models (MRMs) trained with reinforcement learning with verifiable rewards (RLVR) show improved accuracy on visual reasoning benchmarks. However, we observe that accuracy gains often come at the cost of reasoning quality: generated Chain-of-Thought (CoT) traces are frequently inconsistent with the final answer and poorly grounded in the visual evidence. We systematically study this phenomenon across seven challenging real-world spatial reasoning benchmarks and find that it affects contemporary MRMs such as ViGoRL-Spatial, TreeVGR as well as our own models trained with standard Group Relative Policy Optimization (GRPO). We characterize CoT reasoning quality along two complementary axes: "logical consistency" (does the CoT entail the final answer?) and "visual grounding" (does each reasoning step accurately describe objects, attributes, and spatial relationships in the image?). To address this, we propose Faithful GRPO (FGRPO), a variant of GRPO that enforces consistency and grounding as constraints via Lagrangian dual ascent. FGRPO incorporates batch-level consistency and grounding constraints into the advantage computation within a group, adaptively adjusting the relative importance of constraints during optimization. We evaluate FGRPO on Qwen2.5-VL-7B and 3B backbones across seven spatial datasets. Our results show that FGRPO substantially improves reasoning quality, reducing the inconsistency rate from 24.5% to 1.7% and improving visual grounding scores by +13%. It also improves final answer accuracy over simple GRPO, demonstrating that faithful reasoning enables better answers.

Spatial reasoning is a cornerstone capability for intelligent systems to perceive and interact with the physical world. However, multimodal large language models (MLLMs) frequently suffer from hallucinations and imprecision when parsing complex geometric layouts. As data-driven scaling struggles to internalize structured geometric priors and spatial constraints, integrating mature, specialized vision models presents a compelling alternative. Despite its promise, applying this paradigm to spatial reasoning is hindered by two key challenges: The difficulty of invoking heterogeneous, parameter-rich tools, as well as the challenge of understanding and effectively leveraging their diverse low-level outputs (e.g., segmentation masks, depth maps) in high-level reasoning. To address these challenges, we propose LAST, a unified framework for tool-augmented spatial reasoning. LAST features an extensible interactive sandbox, termed LAST-Box, which abstracts heterogeneous tool invocations into atomic instructions and reusable spatial skills, returning multimodal hints (e.g., annotated images and textual descriptions) that can be directly consumed by LLMs. We further design a three-stage progressive training strategy that guides models from understanding tool outputs to proficient and adaptive tool invocation. Experiments on four datasets show that LAST-7B achieves around 20% performance gains over its backbone and outperforms strong proprietary closed-source LLMs, substantially enhancing reasoning on complex spatial tasks.

Synergistic spatial intelligence between UAVs and satellites is indispensable for emergency response and security operations, as it uniquely integrates macro-scale global coverage with dynamic, real-time local perception. However, the capacity of Vision-Language Models (VLMs) to master this complex interplay remains largely unexplored. This gap persists primarily because existing benchmarks are confined to isolated Unmanned Aerial Vehicle (UAV) videos or static satellite imagery, failing to evaluate the dynamic local-to-global spatial mapping essential for comprehensive cross-view reasoning. To bridge this gap, we introduce LinkS$^2$Bench, the first comprehensive benchmark designed to evaluate VLMs' wide-area, dynamic cross-view spatial intelligence. LinkS$^2$Bench links 1,022 minutes of dynamic UAV footage with high-resolution satellite imagery covering over 200 km$^2$. Through an LMM-assisted pipeline and rigorous human annotation, we constructed 17.9k high-quality question-answer pairs comprising 12 fine-grained tasks across four dimensions: perception, localization, relation, and reasoning. Evaluations of 18 representative VLMs reveal a substantial gap compared to human baselines, identifying accurate cross-view dynamic alignment as the critical bottleneck. To alleviate this, we design a Cross-View Alignment Adapter, demonstrating that explicit alignment significantly improves model performance. Furthermore, fine-tuning experiments underscore the potential of LinkS$^2$Bench in advancing VLM adaptation for complex spatial reasoning.

Vision-language models (VLMs) have achieved impressive results on single-view vision tasks, but lack the multi-view spatial reasoning capabilities essential for embodied AI systems to understand 3D environments and manipulate objects across different viewpoints. In this work, we introduce Cross-View Relations (XVR), a large-scale dataset designed to teach VLMs spatial reasoning across multiple views. XVR comprises 100K vision-question-answer samples derived from 18K diverse 3D scenes and 70K robotic manipulation trajectories, spanning three fundamental spatial reasoning tasks: Correspondence (matching objects across views), Verification (validating spatial relationships), and Localization (identifying object positions). VLMs fine-tuned on XVR achieve substantial improvements on established multi-view and robotic spatial reasoning benchmarks (MindCube and RoboSpatial). When integrated as backbones in Vision-Language-Action models, XVR-trained representations improve success rates on RoboCasa. Our results demonstrate that explicit training on cross-view spatial relations significantly enhances multi-view reasoning and transfers effectively to real-world robotic manipulation.

We introduce PerceptionComp, a manually annotated benchmark for complex, long-horizon, perception-centric video reasoning. PerceptionComp is designed so that no single moment is sufficient: answering each question requires multiple temporally separated pieces of visual evidence and compositional constraints under conjunctive and sequential logic, spanning perceptual subtasks such as objects, attributes, relations, locations, actions, and events, and requiring skills including semantic recognition, visual correspondence, temporal reasoning, and spatial reasoning. The benchmark contains 1,114 highly complex questions on 279 videos from diverse domains including city walk tours, indoor villa tours, video games, and extreme outdoor sports, with 100% manual annotation. Human studies show that PerceptionComp requires substantial test-time thinking and repeated perception steps: participants take much longer than on prior benchmarks, and accuracy drops to near chance (18.97%) when rewatching is disallowed. State-of-the-art MLLMs also perform substantially worse on PerceptionComp than on existing benchmarks: the best model in our evaluation, Gemini-3-Flash, reaches only 45.96% accuracy in the five-choice setting, while open-source models remain below 40%. These results suggest that perception-centric long-horizon video reasoning remains a major bottleneck, and we hope PerceptionComp will help drive progress in perceptual reasoning.

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/.

How do multimodal models solve visual spatial tasks -- through genuine planning, or through brute-force search in token space? We introduce MazeBench, a benchmark of 110 procedurally generated maze images across nine controlled groups, and evaluate 16 model configurations from OpenAI, Anthropic, Google, and Alibaba. GPT-5.4 solves 91% and Gemini 3.1 Pro 79%, but these scores are misleading: models typically translate images into text grids and then enumerate paths step by step, consuming 1,710--22,818 tokens per solve for a task humans do quickly. Without added reasoning budgets, all configurations score only 2--12%; on 20$\times$20 ultra-hard mazes, they hit token limits and fail. Qualitative traces reveal a common two-stage strategy: image-to-grid translation followed by token-level search, effectively BFS in prose. A text-grid ablation shows Claude Sonnet 4.6 rising from 6% on images to 80% when given the correct grid, isolating weak visual extraction from downstream search. When explicitly instructed not to construct a grid or perform graph search, models still revert to the same enumeration strategy. MazeBench therefore shows that high accuracy on visual planning tasks does not imply human-like spatial understanding.

Spatial understanding is fundamental for embodied agents, yet most spatial VLMs and benchmarks remain offline-evaluating post-hoc QA over pre-recorded inputs and overlooking two crucial deployment-critical requirements: long-horizon streaming inference and active perception when the current view is insufficient. To address this gap, we introduce S3-Bench, a benchmark suite for streaming spatial question answering with active exploration, where queries are temporally grounded to specific timestamps and must be answered using only observations available up to that moment. S3-Bench adopts a dual-domain design, combining a scalable simulator with controllable trajectories and exploration actions, and real-world streaming videos that capture practical sensing artifacts for rigorous generalization evaluation. Overall, it spans 10K+ scenes and 26K+ trajectories, with dedicated training (S3-Train) and evaluation (S3-Eval) splits. We further propose AMF-VLM, which supports streaming spatial reasoning under bounded computing via (i) memory folding, which compresses long-horizon observations into compact structured memory, and (ii) active exploration, which outputs explicit actions (e.g. move/rotate/scan) to acquire missing evidence before answering. Extensive experiments demonstrate that, compared to models using identical training data, our approach yields improvements of 8.8% and 13.3% on the simulated and real splits of S3-Eval, respectively, while maintaining competitive transferability to standard spatial benchmarks.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, yet they struggle with spatial tasks that require mental simulation, such as mental rotation. This paper investigates whether equipping an LLM with an external Imagery Module'' -- a tool capable of rendering and rotating 3D models -- can bridge this gap, functioning as a cognitive prosthetic.'' We conducted experiments using a dual-module architecture in which a reasoning module (an MLLM) interacts with an imagery module on 3D model rotation tasks. Performance was lower than expected, with accuracy reaching at most 62.5%. Further investigation suggests that even when the burden of maintaining and manipulating a holistic 3D state is outsourced, the system still fails. This reveals that current frontier models lack the foundational visual-spatial primitives required to interface with imagery. Specifically, they lack: (1) the low-level sensitivity to extract spatial signals such as (a) depth, (b) motion, and (c) short-horizon dynamic prediction; and (2) the capacity to reason contemplatively over images, dynamically shifting visual focus and balancing imagery with symbolic and associative information.

Multimodal Large Language Models (MLLMs) have recently demonstrated remarkable perceptual and reasoning abilities. However, they struggle to perceive fine-grained geometric structures, constraining their ability of geometric understanding and visual reasoning. To address this, we propose GeoTikzBridge, a framework that enhances local geometric perception and visual reasoning through tikz-based code generation. Within this framework, we build two models supported by two complementary datasets. The GeoTikzBridge-Base model is trained on GeoTikz-Base dataset, the largest image-to-tikz dataset to date with 2.5M pairs (16 $\times$ larger than existing open-sourced datasets). This process is achieved via iterative data expansion and a localized geometric transformation strategy. Subsequently, GeoTikzBridge-Instruct is fine-tuned on GeoTikz-Instruct dataset which is the first instruction-augmented tikz dataset supporting visual reasoning. Extensive experimental results demonstrate that our models achieve state-of-the-art performance among open-sourced MLLMs. Furthermore, GeoTikzBridge models can serve as plug-and-play reasoning modules for any MLLM(LLM), enhancing reasoning performance in geometric problem-solving. Datasets and codes are publicly available at: https://github.com/sjy-1995/GeoTikzBridge.

Despite the widespread adoption of MLLMs in embodied agents, their capabilities remain largely confined to reactive planning from immediate observations, consistently failing in spatial reasoning across extensive spatiotemporal scales. Cognitive science reveals that Biological Intelligence (BI) thrives on "mental navigation": the strategic construction of spatial representations from experience and the subsequent mental simulation of paths prior to action. To bridge the gap between AI and BI, we introduce Video2Mental, a pioneering benchmark for evaluating the mental navigation capabilities of MLLMs. The task requires constructing hierarchical cognitive maps from long egocentric videos and generating landmark-based path plans step by step, with planning accuracy verified through simulator-based physical interaction. Our benchmarking results reveal that mental navigation capability does not naturally emerge from standard pre-training. Frontier MLLMs struggle profoundly with zero-shot structured spatial representation, and their planning accuracy decays precipitously over extended horizons. To overcome this, we propose NavMind, a reasoning model that internalizes mental navigation using explicit, fine-grained cognitive maps as learnable intermediate representations. Through a difficulty-stratified progressive supervised fine-tuning paradigm, NavMind effectively bridges the gap between raw perception and structured planning. Experiments demonstrate that NavMind achieves superior mental navigation capabilities, significantly outperforming frontier commercial and spatial MLLMs.

Despite remarkable advances in large Vision-Language Models (VLMs), spatial reasoning remains a persistent challenge. In this work, we investigate how attention heads within VLMs contribute to spatial reasoning by analyzing their functional roles through a mechanistic interpretability lens. We introduce CogVSR, a dataset that decomposes complex spatial reasoning questions into step-by-step subquestions designed to simulate human-like reasoning via a chain-of-thought paradigm, with each subquestion linked to specific cognitive functions such as spatial perception or relational reasoning. Building on CogVSR, we develop a probing framework to identify and characterize attention heads specialized for these functions. Our analysis across diverse VLM families reveals that these functional heads are universally sparse, vary in number and distribution across functions. Notably, spatially specialized heads are fewer than those for other cognitive functions, highlighting their scarcity. We propose methods to activate latent spatial heads, improving spatial understanding. Intervention experiments further demonstrate their critical role in spatial reasoning: removing functional heads leads to performance degradation, while emphasizing them enhances accuracy. This study provides new interpretability driven insights into how VLMs attend to space and paves the way for enhancing complex spatial reasoning in multimodal models.

Large Vision Language Models (LVLMs) excel at semantic understanding but struggle with fine grained spatial grounding, as the model must implicitly infer complex geometry without ever producing a spatial interpretation. We present Perceptio, a perception enhanced LVLM with 2D and 3D spatial reasoning abilities, enabled via explicit semantic segmentation tokens and depth tokens generated directly within the autoregressive sequence. Concretely, we (i) distill a VQVAE depth codebook from a strong monocular teacher to tokenize dense depth into compact sequences, and (ii) integrate SAM2 based semantic segmentation tokens and VQ-VAE depth tokens inside the LLM so the model first emits spatial tokens and then answers. To stabilize depth token generation, we introduce novel composite depth-token objectives (marker, token, and count losses) and a soft-merging technique for differentiable reconstruction. We adopt a multi-task co-training strategy across diverse datasets, letting the model learn perception tokens to tackle multiple downstream tasks. Building on InternVL, Perceptio achieves state-of-the-art performance across benchmarks: improving referring expression segmentation by +0.8/+1.4/+1.1 cIoU on RefCOCO/+/g HardBLINK spatial understanding accuracy by 10.3%, and MMBench accuracy by 1.0%, demonstrating that explicit spatial chain-of-thought materially strengthens spatial grounding in LVLMs.

Geometric reasoning inherently requires "thinking with constructions" -- the dynamic manipulation of visual aids to bridge the gap between problem conditions and solutions. However, existing Multimodal Large Language Models (MLLMs) are largely confined to passive inference with static diagrams, lacking the strategic knowledge of when and how to construct effective visual aids. To address this, we present a framework for Visual-Text Interleaved Chain-of-Thought. We first introduce GeoAux-Bench, the first benchmark comprising 4,334 geometry problems that aligns textual construction steps with ground-truth visual updates. Our pilot study reveals two critical insights: (1) interleaved visual-textual aids outperform single-modality counterparts, which cannot losslessly capture geometric synergy; and (2) valid constructions act as entropy reducers, strongly correlating with reduced reasoning perplexity. Building on these findings, we propose Action Applicability Policy Optimization (A2PO), a reinforcement learning paradigm for mastering strategic construction. A2PO employs Adaptive Reward Shaping to regulate the timing and quality of visual aids via counterfactual sampling to distinguish necessary from redundant constructions. Experiments demonstrate our approach enables MLLMs to leverage selective auxiliary constructions, yielding a 3.51% gain over strong baselines. Code and data are available on GitHub.