Daily Papers

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.

Instance-level object segmentation across disparate egocentric and exocentric views is a fundamental challenge in visual understanding, critical for applications in embodied AI and remote collaboration. This task is exceptionally difficult due to severe changes in scale, perspective, and occlusion, which destabilize direct pixel-level matching. While recent geometry-aware models like VGGT provide a strong foundation for feature alignment, we find they often fail at dense prediction tasks due to significant pixel-level projection drift, even when their internal object-level attention remains consistent. To bridge this gap, we introduce VGGT-Segmentor (VGGT-S), a framework that unifies robust geometric modeling with pixel-accurate semantic segmentation. VGGT-S leverages VGGT's powerful cross-view feature representation and introduces a novel Union Segmentation Head. This head operates in three stages: mask prompt fusion, point-guided prediction, and iterative mask refinement, effectively translating high-level feature alignment into a precise segmentation mask. Furthermore, we propose a single-image self-supervised training strategy that eliminates the need for paired annotations and enables strong generalization. On the Ego-Exo4D benchmark, VGGT-S sets a new state-of-the-art, achieving 67.7% and 68.0% average IoU for Ego to Exo and Exo to Ego tasks, respectively, significantly outperforming prior methods. Notably, our correspondence-free pretrained model surpasses most fully-supervised baselines, demonstrating the effectiveness and scalability of our approach.

A new research framework is proposed to incorporate machine learning techniques into the field of experimental chemistry to facilitate chromatographic enantioseparation. A documentary dataset of chiral molecular retention times (CMRT dataset) in high-performance liquid chromatography is established to handle the challenge of data acquisition. Based on the CMRT dataset, a quantile geometry-enhanced graph neural network is proposed to learn the molecular structure-retention time relationship, which shows a satisfactory predictive ability for enantiomers. The domain knowledge of chromatography is incorporated into the machine learning model to achieve multi-column prediction, which paves the way for chromatographic enantioseparation prediction by calculating the separation probability. Experiments confirm that the proposed research framework works well in retention time prediction and chromatographic enantioseparation facilitation, which sheds light on the application of machine learning techniques to the experimental scene and improves the efficiency of experimenters to speed up scientific discovery.

Text-driven Referring Video Object Segmentation (RVOS) aims to locate and segment target objects in videos given natural language. However, existing models are typically trained on 2D image or video datasets with naive segmentation losses, which overlooks the geometric consistency across frames and leads to weak spatial understanding. In this paper, we propose Geometry-enhanced Language-guided Video segmentation (GeoLaV), a two-stage framework that distills 3D geometric knowledge from images to enhance text-driven video segmentation. In the first stage, we perform monocular geometry pretraining with monocular novel-view synthesis, enabling the model to acquire geometry-consistent visual representations via spatial alignment on large-scale single-image datasets. In the second stage, we introduce geometry-aware distillation and fine-tune the model on video segmentation datasets, transferring 3D structural knowledge from a general 3D prior model. This process reinforces 3D awareness and improves both spatiotemporal coherence and language grounding in segmentation. Extensive experiments show that our method using only image segmentation data already provides notable zero-shot generalization in RVOS. When combined with geometry-aware distillation for fine-tuning on videos, our method achieves state-of-the-art performance across multiple RVOS benchmarks. The code is available at https://github.com/Tony1882880/GeoLaV.

We present MG-Nav (Memory-Guided Navigation), a dual-scale framework for zero-shot visual navigation that unifies global memory-guided planning with local geometry-enhanced control. At its core is the Sparse Spatial Memory Graph (SMG), a compact, region-centric memory where each node aggregates multi-view keyframe and object semantics, capturing both appearance and spatial structure while preserving viewpoint diversity. At the global level, the agent is localized on SMG and a goal-conditioned node path is planned via an image-to-instance hybrid retrieval, producing a sequence of reachable waypoints for long-horizon guidance. At the local level, a navigation foundation policy executes these waypoints in point-goal mode with obstacle-aware control, and switches to image-goal mode when navigating from the final node towards the visual target. To further enhance viewpoint alignment and goal recognition, we introduce VGGT-adapter, a lightweight geometric module built on the pre-trained VGGT model, which aligns observation and goal features in a shared 3D-aware space. MG-Nav operates global planning and local control at different frequencies, using periodic re-localization to correct errors. Experiments on HM3D Instance-Image-Goal and MP3D Image-Goal benchmarks demonstrate that MG-Nav achieves state-of-the-art zero-shot performance and remains robust under dynamic rearrangements and unseen scene conditions.

Visual Geometry Grounded Transformers (VGGT) have set new benchmarks in high-fidelity 3D scene reconstruction. However, as the sequence length increases, these models suffer from catastrophic geometric forgetting and accumulation drift, primarily due to the quadratic complexity of global attention which necessitates truncated temporal windows. To overcome the resulting geometric drift, we present Mamba-VGGT, an enhanced VGGT framework capable of persistent long-range reasoning. Our key contribution is a Sliding Window Mamba (SWM) memory module that maintains an explicit external memory token across temporal windows. This module leverages selective state-space modeling to distill and propagate global geometric priors, effectively bypassing the memory constraints of traditional transformers. To integrate these long-term temporal cues without disrupting the highly optimized spatial features of the pre-trained VGGT, we propose a Zero-Init Spatial Memory Injector. Utilizing zero-convolutional layers, this injector adaptively fuses persistent memory into the patch token stream, ensuring structural stability and seamless feature alignment. Extensive experiments demonstrate that our approach significantly outperforms existing VGGT-based methods in maintaining spatial consistency and reducing trajectory accumulation errors. Our work provides a scalable, linear-complexity solution for geometry-grounded world modeling in extensive 3D environments.

In this work, we study an integrated fault detection and classification framework called FARM for fast, accurate, and robust online chemical process monitoring. The FARM framework integrates the latest advancements in statistical process control (SPC) for monitoring nonparametric and heterogeneous data streams with novel data analysis approaches based on Riemannian geometry together in a hierarchical framework for online process monitoring. We conduct a systematic evaluation of the FARM monitoring framework using the Tennessee Eastman Process (TEP) dataset. Results show that FARM performs competitively against state-of-the-art process monitoring algorithms by achieving a good balance among fault detection rate (FDR), fault detection speed (FDS), and false alarm rate (FAR). Specifically, FARM achieved an average FDR of 96.97% while also outperforming benchmark methods in successfully detecting hard-to-detect faults that are previously known, including Faults 3, 9 and 15, with FDRs being 97.08%, 96.30% and 95.99%, respectively. In terms of FAR, our FARM framework allows practitioners to customize their choice of FAR, thereby offering great flexibility. Moreover, we report a significant improvement in average fault classification accuracy during online monitoring from 61% to 82% when leveraging Riemannian geometric analysis, and further to 84.5% when incorporating additional features from SPC. This illustrates the synergistic effect of integrating fault detection and classification in a holistic, hierarchical monitoring framework.

Tuning-free approaches adapting large-scale pre-trained video diffusion models for identity-preserving text-to-video generation (IPT2V) have gained popularity recently due to their efficacy and scalability. However, significant challenges remain to achieve satisfied facial dynamics while keeping the identity unchanged. In this work, we present a novel tuning-free IPT2V framework by enhancing face knowledge of the pre-trained video model built on diffusion transformers (DiT), dubbed FantasyID. Essentially, 3D facial geometry prior is incorporated to ensure plausible facial structures during video synthesis. To prevent the model from learning copy-paste shortcuts that simply replicate reference face across frames, a multi-view face augmentation strategy is devised to capture diverse 2D facial appearance features, hence increasing the dynamics over the facial expressions and head poses. Additionally, after blending the 2D and 3D features as guidance, instead of naively employing cross-attention to inject guidance cues into DiT layers, a learnable layer-aware adaptive mechanism is employed to selectively inject the fused features into each individual DiT layers, facilitating balanced modeling of identity preservation and motion dynamics. Experimental results validate our model's superiority over the current tuning-free IPT2V methods.

Recently, 3D Gaussian splatting (3D-GS) has achieved great success in reconstructing and rendering real-world scenes. To transfer the high rendering quality to generation tasks, a series of research works attempt to generate 3D-Gaussian assets from text. However, the generated assets have not achieved the same quality as those in reconstruction tasks. We observe that Gaussians tend to grow without control as the generation process may cause indeterminacy. Aiming at highly enhancing the generation quality, we propose a novel framework named GaussianDreamerPro. The main idea is to bind Gaussians to reasonable geometry, which evolves over the whole generation process. Along different stages of our framework, both the geometry and appearance can be enriched progressively. The final output asset is constructed with 3D Gaussians bound to mesh, which shows significantly enhanced details and quality compared with previous methods. Notably, the generated asset can also be seamlessly integrated into downstream manipulation pipelines, e.g. animation, composition, and simulation etc., greatly promoting its potential in wide applications. Demos are available at https://taoranyi.com/gaussiandreamerpro/.

Reinforcement learning (RL) is a central approach for improving reasoning capabilities in large language models (LLMs), where training efficiency depends critically on how problems are sampled during optimization. Existing adaptive curriculum learning methods typically prioritize prompts of intermediate difficulty, treating problem selection as a standard bandit problem with independent arms and overlooking the structured, heterogeneous nature of the task space. In this work, we frame problem sampling as a manifold-structured bandit problem with endogenous non-stationarity: problems are related through the model's latent representation space, and sampling decisions can steer how learning signals evolve across that space. To operationalize this perspective, we introduce Bayesian Manifold Curriculum (BMC), a structure-aware framework that organizes problems into a hierarchical task tree and applies Bayesian learning to guide sampling. Empirically, we find that different sampling strategies induce non-trivial tradeoffs between productivity (learning signal), diversity (coverage of the task manifold), and utility (evaluation relevance). These results show that prioritizing difficulty alone is insufficient for strong downstream performance, highlighting the importance of incorporating structure and type-awareness into problem sampling.

Creating dynamic, view-consistent videos of customized subjects is highly sought after for a wide range of emerging applications, including immersive VR/AR, virtual production, and next-generation e-commerce. However, despite rapid progress in subject-driven video generation, existing methods predominantly treat subjects as 2D entities, focusing on transferring identity through single-view visual features or textual prompts. Because real-world subjects are inherently 3D, applying these 2D-centric approaches to 3D object customization reveals a fundamental limitation: they lack the comprehensive spatial priors necessary to reconstruct the 3D geometry. Consequently, when synthesizing novel views, they must rely on generating plausible but arbitrary details for unseen regions, rather than preserving the true 3D identity. Achieving genuine 3D-aware customization remains challenging due to the scarcity of multi-view video datasets. While one might attempt to fine-tune models on limited video sequences, this often leads to temporal overfitting. To resolve these issues, we introduce a novel framework for 3D-aware video customization, comprising 3DreamBooth and 3Dapter. 3DreamBooth decouples spatial geometry from temporal motion through a 1-frame optimization paradigm. By restricting updates to spatial representations, it effectively bakes a robust 3D prior into the model without the need for exhaustive video-based training. To enhance fine-grained textures and accelerate convergence, we incorporate 3Dapter, a visual conditioning module. Following single-view pre-training, 3Dapter undergoes multi-view joint optimization with the main generation branch via an asymmetrical conditioning strategy. This design allows the module to act as a dynamic selective router, querying view-specific geometric hints from a minimal reference set. Project page: https://ko-lani.github.io/3DreamBooth/

Urban scene reconstruction requires modeling both static infrastructure and dynamic elements while supporting diverse environmental conditions. We present StyledStreets, a multi-style street simulator that achieves instruction-driven scene editing with guaranteed spatial and temporal consistency. Building on a state-of-the-art Gaussian Splatting framework for street scenarios enhanced by our proposed pose optimization and multi-view training, our method enables photorealistic style transfers across seasons, weather conditions, and camera setups through three key innovations: First, a hybrid embedding scheme disentangles persistent scene geometry from transient style attributes, allowing realistic environmental edits while preserving structural integrity. Second, uncertainty-aware rendering mitigates supervision noise from diffusion priors, enabling robust training across extreme style variations. Third, a unified parametric model prevents geometric drift through regularized updates, maintaining multi-view consistency across seven vehicle-mounted cameras. Our framework preserves the original scene's motion patterns and geometric relationships. Qualitative results demonstrate plausible transitions between diverse conditions (snow, sandstorm, night), while quantitative evaluations show state-of-the-art geometric accuracy under style transfers. The approach establishes new capabilities for urban simulation, with applications in autonomous vehicle testing and augmented reality systems requiring reliable environmental consistency. Codes will be publicly available upon publication.

Recent advances in diffusion-based video generation have opened new possibilities for controllable video editing, yet realistic video object insertion (VOI) remains challenging due to limited 4D scene understanding and inadequate handling of occlusion and lighting effects. We present InsertAnywhere, a new VOI framework that achieves geometrically consistent object placement and appearance-faithful video synthesis. Our method begins with a 4D aware mask generation module that reconstructs the scene geometry and propagates user specified object placement across frames while maintaining temporal coherence and occlusion consistency. Building upon this spatial foundation, we extend a diffusion based video generation model to jointly synthesize the inserted object and its surrounding local variations such as illumination and shading. To enable supervised training, we introduce ROSE++, an illumination aware synthetic dataset constructed by transforming the ROSE object removal dataset into triplets of object removed video, object present video, and a VLM generated reference image. Through extensive experiments, we demonstrate that our framework produces geometrically plausible and visually coherent object insertions across diverse real world scenarios, significantly outperforming existing research and commercial models.

Foundation features from self-supervised vision models and text-to-image diffusion models have proven effective for semantic correspondence estimation. However, because these features are learned primarily from 2D image objectives, they lack explicit 3D awareness and often confuse symmetric object sides, repeated parts, and visually similar structures that are distinct in 3D. We introduce a 3D-aware post-training framework that goes beyond available 2D foundation features by incorporating priors from 3D foundation models. Given an image, our method uses SAM3D to estimate object geometry and pose, and refines the pose through render-and-compare optimization. Subsequently, we render PartField descriptors from the reconstructed geometry into the image plane based on the estimated object pose. The resulting geometry-aware feature maps complement DINO and Stable Diffusion features, while geodesic distances on the reconstructed shapes enable reliable filtering of candidate correspondences. We use the filtered matches as supervision to train a lightweight adapter on top of DINO and Stable Diffusion for semantic correspondence. In contrast to prior post-training approaches that require pose annotations and rely on coarse spherical geometry, our method automatically obtains instance-specific 3D structure and uses it to guide correspondence learning. Experiments show that our approach improves semantic correspondence over the prior methods while reducing manual geometric supervision. Code and model can be found at https:/github.com/GenIntel/3D-SC.

Recent World Action Models (WAMs) have demonstrated impressive capabilities in embodied decision-making. However, whether their effectiveness stems from explicit future imagination during inference or representation learning induced by predictive training remains an open question. Emerging evidence suggests the primary advantage lies in learning robust latent representations rather than generating future observations at test time. Nevertheless, existing WAMs mainly rely on RGB-based future prediction, which provides limited structural and spatial understanding of complex environments. To address this, we propose a structured world modeling framework that enhances latent representations through geometric and semantic supervision. Alongside future RGB prediction, our model introduces two auxiliary prediction branches for future geometry and semantic representations, enabling it to jointly capture scene dynamics, spatial geometry, and semantic context within a unified latent space. Crucially, our approach preserves efficient inference by avoiding explicit future rollout or video generation at test time. Extensive experiments show that incorporating structured world supervision consistently improves action prediction accuracy, scene understanding, and robustness under challenging embodied scenarios, highlighting its potential for advancing scalable and efficient WAMs.

Industrial quality inspection plays a critical role in modern manufacturing by identifying defective products during production. While single-modality approaches using either 3D point clouds or 2D RGB images suffer from information incompleteness, multimodal anomaly detection offers promise through the complementary fusion of crossmodal data. However, existing methods face challenges in effectively integrating unimodal results and improving discriminative power. To address these limitations, we first reinterpret memory bank-based anomaly scores in single modalities as isotropic Euclidean distances in local feature spaces. Dynamically evolving from Euclidean metrics, we propose a novel Geometry-Guided Score Fusion (G^{2}SF) framework that progressively learns an anisotropic local distance metric as a unified score for the fusion task. Through a geometric encoding operator, a novel Local Scale Prediction Network (LSPN) is proposed to predict direction-aware scaling factors that characterize first-order local feature distributions, thereby enhancing discrimination between normal and anomalous patterns. Additionally, we develop specialized loss functions and score aggregation strategy from geometric priors to ensure both metric generalization and efficacy. Comprehensive evaluations on the MVTec-3D AD and Eyecandies datasets demonstrate the state-of-the-art detection performance of our method, and detailed ablation analysis validates each component's contribution. Our code is available at https://github.com/ctaoaa/G2SF.

Trajectory planning in unstructured environments is a fundamental and challenging capability for mobile robots. Traditional modular pipelines suffer from latency and cascading errors across perception, localization, mapping, and planning modules. Recent end-to-end learning methods map raw visual observations directly to control signals or trajectories, promising greater performance and efficiency in open-world settings. However, most prior end-to-end approaches still rely on separate localization modules that depend on accurate sensor extrinsic calibration for self-state estimation, thereby limiting generalization across embodiments and environments. We introduce LoGoPlanner, a localization-grounded, end-to-end navigation framework that addresses these limitations by: (1) finetuning a long-horizon visual-geometry backbone to ground predictions with absolute metric scale, thereby providing implicit state estimation for accurate localization; (2) reconstructing surrounding scene geometry from historical observations to supply dense, fine-grained environmental awareness for reliable obstacle avoidance; and (3) conditioning the policy on implicit geometry bootstrapped by the aforementioned auxiliary tasks, thereby reducing error propagation.We evaluate LoGoPlanner in both simulation and real-world settings, where its fully end-to-end design reduces cumulative error while metric-aware geometry memory enhances planning consistency and obstacle avoidance, leading to more than a 27.3\% improvement over oracle-localization baselines and strong generalization across embodiments and environments. The code and models have been made publicly available on the https://steinate.github.io/logoplanner.github.io/{project page}.

Dual-Encoders is a promising mechanism for answer retrieval in question answering (QA) systems. Currently most conventional Dual-Encoders learn the semantic representations of questions and answers merely through matching score. Researchers proposed to introduce the QA interaction features in scoring function but at the cost of low efficiency in inference stage. To keep independent encoding of questions and answers during inference stage, variational auto-encoder is further introduced to reconstruct answers (questions) from question (answer) embeddings as an auxiliary task to enhance QA interaction in representation learning in training stage. However, the needs of text generation and answer retrieval are different, which leads to hardness in training. In this work, we propose a framework to enhance the Dual-Encoders model with question answer cross-embeddings and a novel Geometry Alignment Mechanism (GAM) to align the geometry of embeddings from Dual-Encoders with that from Cross-Encoders. Extensive experimental results show that our framework significantly improves Dual-Encoders model and outperforms the state-of-the-art method on multiple answer retrieval datasets.

Video world models aim to simulate controllable visual environments, but long-horizon rollouts depend on what the model remembers after observations leave its native context window. Explicit memories retain frames or online 3D reconstructions, which can suffer from heuristic retrieval errors, redundant appearance storage, or reconstruction artifacts. Implicit memories compress history into a compact state, but existing designs are not explicitly constrained to encode cross-view scene geometry. We propose GIM-World, a geometry-aware implicit memory framework for video world models. A lightweight transformer encoder compresses variable-length history into fixed-size memory tokens, a camera-queryable geometry head distills 3D scene structure from a frozen foundation model into the memory during training, and an information-guided pruning rule keeps encoding cost bounded as history grows. The geometry teacher is discarded at inference, leaving a lightweight memory module. Experiments on MIND show that GIM-World better preserves long-horizon geometric and visual consistency than both explicit- and implicit-memory baselines.

Bird's-Eye-View (BEV) perception serves as a cornerstone for autonomous driving, offering a unified spatial representation that fuses surrounding-view images to enable reasoning for various downstream tasks, such as semantic segmentation, 3D object detection, and motion prediction. However, most existing BEV perception frameworks adopt an end-to-end training paradigm, where image features are directly transformed into the BEV space and optimized solely through downstream task supervision. This formulation treats the entire perception process as a black box, often lacking explicit 3D geometric understanding and interpretability, leading to suboptimal performance. In this paper, we claim that an explicit 3D representation matters for accurate BEV perception, and we propose Splat2BEV, a Gaussian Splatting-assisted framework for BEV tasks. Splat2BEV aims to learn BEV feature representations that are both semantically rich and geometrically precise. We first pre-train a Gaussian generator that explicitly reconstructs 3D scenes from multi-view inputs, enabling the generation of geometry-aligned feature representations. These representations are then projected into the BEV space to serve as inputs for downstream tasks. Extensive experiments on nuScenes and argoverse dataset demonstrate that Splat2BEV achieves state-of-the-art performance and validate the effectiveness of incorporating explicit 3D reconstruction into BEV perception.

Multimodal Large Language Models (MLLMs) have achieved remarkable progress in 2D visual tasks but still exhibit limited physical spatial awareness when processing real-world visual streams. Recently, feed-forward geometric foundation models, which implicitly extract geometric priors, have provided a new pathway to address this issue. However, existing geometry-aware MLLMs are predominantly constrained by the paradigm of single deep-layer extraction and input-level fusion. This flattened fusion leads to the loss of local geometric details and causes semantic mismatches in the early layers. To break this bottleneck, we propose GUIDE (Geometric Unrolling Inside MLLM Early-layers), a progressive geometric priors injection framework. GUIDE performs multi-level sampling within the geometric encoder, comprehensively capturing multi-granularity features ranging from local edges to global topologies. Subsequently, we rigorously align and fuse these multi-level geometric priors step-by-step with the early layers of the MLLM. Building upon the injection of multi-granularity geometric information, this design guides the model to progressively learn the 2D-to-3D transitional process. Furthermore, we introduce a context-aware gating that enables the model to fetch requisite spatial cues based on current semantics, thereby maximizing the utilization efficiency of spatial priors and effectively suppressing redundant geometric noise. Extensive experiments demonstrate that GUIDE significantly outperforms existing baselines on multiple complex spatial reasoning and perception tasks, establishing a novel paradigm for integrating 3D geometric priors into large models.

Respiratory sound classification is hindered by the limited size, high noise levels, and severe class imbalance of benchmark datasets like ICBHI 2017. While Transformer-based models offer powerful feature extraction capabilities, they are prone to overfitting and often converge to sharp minima in the loss landscape when trained on such constrained medical data. To address this, we introduce a framework that enhances the Audio Spectrogram Transformer (AST) using Sharpness-Aware Minimization (SAM). Instead of merely minimizing the training loss, our approach optimizes the geometry of the loss surface, guiding the model toward flatter minima that generalize better to unseen patients. We also implement a weighted sampling strategy to handle class imbalance effectively. Our method achieves a state-of-the-art score of 68.10% on the ICBHI 2017 dataset, outperforming existing CNN and hybrid baselines. More importantly, it reaches a sensitivity of 68.31%, a crucial improvement for reliable clinical screening. Further analysis using t-SNE and attention maps confirms that the model learns robust, discriminative features rather than memorizing background noise.

Recently, Vision-Language-Action (VLA) models have demonstrated strong generalization across diverse tasks. However, effective robotic manipulation in physical environments fundamentally requires geometric understanding and spatial reasoning. While some VLA approaches attempt to incorporate 3D information, they are constrained by limited data availability and geometric information loss in current 3D encoding pipelines, and fail to jointly capture 3D geometry and temporally structured actions in dynamic environments. To address these limitations, we introduce Lift3D-VLA, a unified VLA framework that equips models with explicit 3D point cloud reasoning and enables temporally coherent action generation. First, building upon our previous work Lift3D, an enhanced 2D model-lifting strategy is proposed to geometrically align 3D points with pretrained 2D positional embeddings. This design enables direct point-cloud encoding within the VLA vision encoder while minimizing spatial information loss. Based on explicit 3D inputs, we propose Geometry-Centric Masked Autoencoding (GC-MAE), a dual-objective self-supervised framework that reconstructs the current point cloud while predicting its future geometric evolution. This formulation allows the 2D vision encoder to internalize both 3D structure and physical dynamics. To fully exploit 3D representations, we further design layer-wise temporal action modeling, which leverages multiple layers of the LLM to collaboratively predict action chunks, enabling temporally consistent predictions. Across 22 simulated tasks and 8 real-world manipulation tasks, Lift3D-VLA achieves 10.8% and 11.1% higher mean success rates on MetaWorld and RLBench than the best-performing prior VLA methods, and outperforms the strongest real-world baseline by 4 percentage points, while exhibiting stronger generalization to out-of-distribution perturbations.

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

Learning-based multi-view stereo (MVS) methods deal with predicting accurate depth maps to achieve an accurate and complete 3D representation. Despite the excellent performance, existing methods ignore the fact that a suitable depth geometry is also critical in MVS. In this paper, we demonstrate that different depth geometries have significant performance gaps, even using the same depth prediction error. Therefore, we introduce an ideal depth geometry composed of Saddle-Shaped Cells, whose predicted depth map oscillates upward and downward around the ground-truth surface, rather than maintaining a continuous and smooth depth plane. To achieve it, we develop a coarse-to-fine framework called Dual-MVSNet (DMVSNet), which can produce an oscillating depth plane. Technically, we predict two depth values for each pixel (Dual-Depth), and propose a novel loss function and a checkerboard-shaped selecting strategy to constrain the predicted depth geometry. Compared to existing methods,DMVSNet achieves a high rank on the DTU benchmark and obtains the top performance on challenging scenes of Tanks and Temples, demonstrating its strong performance and generalization ability. Our method also points to a new research direction for considering depth geometry in MVS.

Auxiliary lines are essential for solving complex geometric problems but remain challenging for large vision-language models (LVLMs). Recent attempts construct auxiliary lines via code-driven rendering, a strategy that relies on accurate and executable code generation to produce visual renderings of the auxiliary lines for subsequent reasoning. However, in complex solid geometry settings, such a strong dependence on precise specifications substantially restricts the robustness of this strategy. Alternatively, we turn to a simpler and more stable solution, representing auxiliary-line constructions as structured textual descriptions. To bridge the gap between textual descriptions and spatial structure, we propose a reinforcement learning framework that enhances diagram-text alignment. The core is a cross-modal reward model that evaluates how well the generated auxiliary-line description matches the ground-truth auxiliary-line diagram. The reward signal drives a GRPO-based RL stage to yield informative auxiliary-line descriptions for the reasoning. To support the training and evaluation, we develop a scalable data pipeline and construct AuxSolidMath, a dataset of 3,018 real-exam geometry problems with paired diagrams and aligned textual fields. Based on this framework, we derive GeoVLMath, an LVLM for solving complex solid geometry.

Stereo matching and surface normal estimation are fundamental tasks in 3D vision. However, existing feed-forward stereo methods still struggle to produce reliable predictions in challenging regions, mainly due to the lack of strong geometric priors. In this paper, we propose GeoStereo, a unified stereo geometry estimation framework that leverages powerful diffusion priors to jointly predict disparity and surface normals. Specifically, GeoStereo couples a feed-forward stereo matching pipeline with a diffusion-based normal estimation branch. To enable effective interaction between the two tasks, we introduce a disparity to normal initialization strategy and construct a warp to left-view condition for the diffusion process. This coupled design allows the diffusion branch to provide strong structural priors that enhance disparity estimation in ill-posed regions, while the feed-forward branch offers reliable geometric guidance for accurate normal prediction. Extensive experiments show that GeoStereo performs reliably in challenging scenarios, including low-light environments, highly reflective surfaces, and transparent objects. Under zero-shot settings, it achieves Rank-1 disparity estimation on multiple benchmarks, including KITTI and NYUv2, and delivers the best normal estimation accuracy on many real indoor benchmarks, such as iBims-1 and ScanNet. Project page: https://qz-wei.github.io/GeoStereo.github.io/

High-quality 3D assets are essential for various applications in computer graphics and 3D vision but remain scarce due to significant acquisition costs. To address this shortage, we introduce Elevate3D, a novel framework that transforms readily accessible low-quality 3D assets into higher quality. At the core of Elevate3D is HFS-SDEdit, a specialized texture enhancement method that significantly improves texture quality while preserving the appearance and geometry while fixing its degradations. Furthermore, Elevate3D operates in a view-by-view manner, alternating between texture and geometry refinement. Unlike previous methods that have largely overlooked geometry refinement, our framework leverages geometric cues from images refined with HFS-SDEdit by employing state-of-the-art monocular geometry predictors. This approach ensures detailed and accurate geometry that aligns seamlessly with the enhanced texture. Elevate3D outperforms recent competitors by achieving state-of-the-art quality in 3D model refinement, effectively addressing the scarcity of high-quality open-source 3D assets.

While recent video diffusion models (VDMs) produce visually impressive results, they fundamentally struggle to maintain 3D structural consistency, often resulting in object deformation or spatial drift. We hypothesize that these failures arise because standard denoising objectives lack explicit incentives for geometric coherence. To address this, we introduce VideoGPA (Video Geometric Preference Alignment), a data-efficient self-supervised framework that leverages a geometry foundation model to automatically derive dense preference signals that guide VDMs via Direct Preference Optimization (DPO). This approach effectively steers the generative distribution toward inherent 3D consistency without requiring human annotations. VideoGPA significantly enhances temporal stability, physical plausibility, and motion coherence using minimal preference pairs, consistently outperforming state-of-the-art baselines in extensive experiments.

Generalized few-shot object detection aims to achieve precise detection on both base classes with abundant annotations and novel classes with limited training data. Existing approaches enhance few-shot generalization with the sacrifice of base-class performance, or maintain high precision in base-class detection with limited improvement in novel-class adaptation. In this paper, we point out the reason is insufficient Discriminative feature learning for all of the classes. As such, we propose a new training framework, DiGeo, to learn Geometry-aware features of inter-class separation and intra-class compactness. To guide the separation of feature clusters, we derive an offline simplex equiangular tight frame (ETF) classifier whose weights serve as class centers and are maximally and equally separated. To tighten the cluster for each class, we include adaptive class-specific margins into the classification loss and encourage the features close to the class centers. Experimental studies on two few-shot benchmark datasets (VOC, COCO) and one long-tail dataset (LVIS) demonstrate that, with a single model, our method can effectively improve generalization on novel classes without hurting the detection of base classes.

Constructing 4D language fields is crucial for embodied AI, augmented/virtual reality, and 4D scene understanding, as they provide enriched semantic representations of dynamic environments and enable open-vocabulary querying in complex scenarios. However, existing approaches to 4D semantic field construction primarily rely on scene-specific Gaussian splatting, which requires per-scene optimization, exhibits limited generalization, and is difficult to scale to real-world applications. To address these limitations, we propose 4DLangVGGT, the first Transformer-based feed-forward unified framework for 4D language grounding, that jointly integrates geometric perception and language alignment within a single architecture. 4DLangVGGT has two key components: the 4D Visual Geometry Transformer, StreamVGGT, which captures spatio-temporal geometric representations of dynamic scenes; and the Semantic Bridging Decoder (SBD), which projects geometry-aware features into a language-aligned semantic space, thereby enhancing semantic interpretability while preserving structural fidelity. Unlike prior methods that depend on costly per-scene optimization, 4DLangVGGT can be jointly trained across multiple dynamic scenes and directly applied during inference, achieving both deployment efficiency and strong generalization. This design significantly improves the practicality of large-scale deployment and establishes a new paradigm for open-vocabulary 4D scene understanding. Experiments on HyperNeRF and Neu3D datasets demonstrate that our approach not only generalizes effectively but also achieves state-of-the-art performance, achieving up to 2% gains under per-scene training and 1% improvements under multi-scene training. Our code released in https://github.com/hustvl/4DLangVGGT

Score distillation sampling (SDS), the methodology in which the score from pretrained 2D diffusion models is distilled into 3D representation, has recently brought significant advancements in text-to-3D generation task. However, this approach is still confronted with critical geometric inconsistency problems such as the Janus problem. Starting from a hypothesis that such inconsistency problems may be induced by multiview inconsistencies between 2D scores predicted from various viewpoints, we introduce GSD, a simple and general plug-and-play framework for incorporating 3D consistency and therefore geometry awareness into the SDS process. Our methodology is composed of three components: 3D consistent noising, designed to produce 3D consistent noise maps that perfectly follow the standard Gaussian distribution, geometry-based gradient warping for identifying correspondences between predicted gradients of different viewpoints, and novel gradient consistency loss to optimize the scene geometry toward producing more consistent gradients. We demonstrate that our method significantly improves performance, successfully addressing the geometric inconsistency problems in text-to-3D generation task with minimal computation cost and being compatible with existing score distillation-based models. Our project page is available at https://ku-cvlab.github.io/GSD/.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

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.

The rapid development of Large Multimodal Models (LMMs) has led to remarkable progress in 2D visual understanding; however, extending these capabilities to 3D scene understanding remains a significant challenge. Existing approaches predominantly rely on text-only supervision, which fails to provide the geometric constraints required for learning robust 3D spatial representations. In this paper, we introduce Reg3D, a novel Reconstructive Geometry Instruction Tuning framework that addresses this limitation by incorporating geometry-aware supervision directly into the training process. Our key insight is that effective 3D understanding necessitates reconstructing underlying geometric structures rather than merely describing them. Unlike existing methods that inject 3D information solely at the input level, Reg3D adopts a dual-supervision paradigm that leverages 3D geometric information both as input and as explicit learning targets. Specifically, we design complementary object-level and frame-level reconstruction tasks within a dual-encoder architecture, enforcing geometric consistency to encourage the development of spatial reasoning capabilities. Extensive experiments on ScanQA, Scan2Cap, ScanRefer, and SQA3D demonstrate that Reg3D delivers substantial performance improvements, establishing a new training paradigm for spatially aware multimodal models.

High-fidelity head avatar reconstruction plays a crucial role in AR/VR, gaming, and multimedia content creation. Recent advances in 3D Gaussian Splatting (3DGS) have demonstrated effectiveness in modeling complex geometry with real-time rendering capability and are now widely used in high-fidelity head avatar reconstruction tasks. However, existing 3DGS-based methods still face significant challenges in capturing fine-grained facial expressions and preserving local texture continuity, especially in highly deformable regions. To mitigate these limitations, we propose a novel 3DGS-based framework termed EAvatar for head reconstruction that is both expression-aware and deformation-aware. Our method introduces a sparse expression control mechanism, where a small number of key Gaussians are used to influence the deformation of their neighboring Gaussians, enabling accurate modeling of local deformations and fine-scale texture transitions. Furthermore, we leverage high-quality 3D priors from pretrained generative models to provide a more reliable facial geometry, offering structural guidance that improves convergence stability and shape accuracy during training. Experimental results demonstrate that our method produces more accurate and visually coherent head reconstructions with improved expression controllability and detail fidelity.

Cross-view localization, the task of estimating a camera's 3-degrees-of-freedom (3-DoF) pose by aligning ground-level images with satellite images, is crucial for large-scale outdoor applications like autonomous navigation and augmented reality. Existing methods often rely on fully supervised learning, which requires costly ground-truth pose annotations. In this work, we propose GeoDistill, a Geometry guided weakly supervised self distillation framework that uses teacher-student learning with Field-of-View (FoV)-based masking to enhance local feature learning for robust cross-view localization. In GeoDistill, the teacher model localizes a panoramic image, while the student model predicts locations from a limited FoV counterpart created by FoV-based masking. By aligning the student's predictions with those of the teacher, the student focuses on key features like lane lines and ignores textureless regions, such as roads. This results in more accurate predictions and reduced uncertainty, regardless of whether the query images are panoramas or limited FoV images. Our experiments show that GeoDistill significantly improves localization performance across different frameworks. Additionally, we introduce a novel orientation estimation network that predicts relative orientation without requiring precise planar position ground truth. GeoDistill provides a scalable and efficient solution for real-world cross-view localization challenges. Code and model can be found at https://github.com/tongshw/GeoDistill.

State-of-the-art embedding models are increasingly derived from decoder-only Large Language Model (LLM) backbones adapted via contrastive learning. Given the emergence of reasoning models trained via Reinforcement Learning with Verifiable Rewards (RLVR), a natural question arises: do enhanced reasoning translate to superior semantic representations when these models serve as embedding initializations? Contrary to expectation, our evaluation on MTEB and BRIGHT reveals a **null effect**: embedding models initialized from RLVR-tuned backbones yield no consistent performance advantage over their base counterparts when subjected to identical training recipes. To unpack this paradox, we introduce **H**ierarchical **R**epresentation **S**imilarity **A**nalysis (HRSA), a framework that decomposes similarity across representation, geometry, and function levels. HRSA reveals that while RLVR induces irreversible latent manifold's local geometry reorganization and reversible coordinate basis drift, it preserves the global manifold geometry and linear readout. Consequently, subsequent contrastive learning drives strong alignment between base- and reasoning-initialized models, a phenomenon we term **Manifold Realignment**. Empirically, our findings suggest that unlike Supervised Fine-Tuning (SFT), RLVR optimizes trajectories within an existing semantic landscape rather than fundamentally restructuring the landscape itself.

Point cloud classification is one of the essential technologies for achieving intelligent perception of 3D environments by machines, its core challenge is to efficiently extract local and global features. Mamba leverages state space models (SSMs) for global point cloud modeling. Although prior Mamba-based point cloud processing methods pay attention to the limitation of its flattened sequence modeling mechanism in fusing local and global features, the critical issue of weakened local geometric relevance caused by decoupling geometric structures and features in the input patches remains not fully revealed, and both jointly limit local feature extraction. Therefore, we propose HyMamba, a geometry and feature coupled Mamba framework featuring: (1) Geometry-Feature Coupled Pooling (GFCP), which achieves physically interpretable geometric information coupling by dynamically aggregating adjacent geometric information into local features; (2) Collaborative Feature Enhancer (CoFE), which enhances sparse signal capture through cross-path feature hybridization while effectively integrating global and local contexts. We conducted extensive experiments on ModelNet40 and ScanObjectNN datasets. The results demonstrate that the proposed model achieves superior classification performance, particularly on the ModelNet40, where it elevates accuracy to 95.99% with merely 0.03M additional parameters. Furthermore, it attains 98.9% accuracy on the ModelNetFewShot dataset, validating its robust generalization capabilities under sparse samples. Our code and weights are available at https://github.com/L1277471578/HyMamba

We present a novel approach for synthesizing 3D talking heads with controllable emotion, featuring enhanced lip synchronization and rendering quality. Despite significant progress in the field, prior methods still suffer from multi-view consistency and a lack of emotional expressiveness. To address these issues, we collect EmoTalk3D dataset with calibrated multi-view videos, emotional annotations, and per-frame 3D geometry. By training on the EmoTalk3D dataset, we propose a `Speech-to-Geometry-to-Appearance' mapping framework that first predicts faithful 3D geometry sequence from the audio features, then the appearance of a 3D talking head represented by 4D Gaussians is synthesized from the predicted geometry. The appearance is further disentangled into canonical and dynamic Gaussians, learned from multi-view videos, and fused to render free-view talking head animation. Moreover, our model enables controllable emotion in the generated talking heads and can be rendered in wide-range views. Our method exhibits improved rendering quality and stability in lip motion generation while capturing dynamic facial details such as wrinkles and subtle expressions. Experiments demonstrate the effectiveness of our approach in generating high-fidelity and emotion-controllable 3D talking heads. The code and EmoTalk3D dataset are released at https://nju-3dv.github.io/projects/EmoTalk3D.

Realistic 3D human generation from text prompts is a desirable yet challenging task. Existing methods optimize 3D representations like mesh or neural fields via score distillation sampling (SDS), which suffers from inadequate fine details or excessive training time. In this paper, we propose an efficient yet effective framework, HumanGaussian, that generates high-quality 3D humans with fine-grained geometry and realistic appearance. Our key insight is that 3D Gaussian Splatting is an efficient renderer with periodic Gaussian shrinkage or growing, where such adaptive density control can be naturally guided by intrinsic human structures. Specifically, 1) we first propose a Structure-Aware SDS that simultaneously optimizes human appearance and geometry. The multi-modal score function from both RGB and depth space is leveraged to distill the Gaussian densification and pruning process. 2) Moreover, we devise an Annealed Negative Prompt Guidance by decomposing SDS into a noisier generative score and a cleaner classifier score, which well addresses the over-saturation issue. The floating artifacts are further eliminated based on Gaussian size in a prune-only phase to enhance generation smoothness. Extensive experiments demonstrate the superior efficiency and competitive quality of our framework, rendering vivid 3D humans under diverse scenarios. Project Page: https://alvinliu0.github.io/projects/HumanGaussian

360 panoramic images are increasingly used in virtual reality, autonomous driving, and robotics for holistic scene understanding. However, current Vision-Language Models (VLMs) struggle with 3D spatial reasoning on Equirectangular Projection (ERP) images due to geometric distortion and limited 3D supervision. We introduce PanoEnv, a large-scale VQA benchmark built from synthetic 3D environments, containing 14.8K questions across five categories (e.g., relative position, volume comparison) grounded in accurate 3D annotations including depth, segmentation, and bounding boxes. Benchmarking 14 state-of-the-art VLMs reveals limited 3D understanding, achieving only 49.34% overall accuracy and 8.36% on open-ended (OE) questions. To enhance 3D reasoning, we propose a reinforcement learning post-training framework based on Group Relative Policy Optimization (GRPO) with a ground-truth-guided reward that incorporates five geometry-aware strategies such as distance tolerance and spatial consistency. A two-stage curriculum further mitigates catastrophic forgetting: Stage 1 trains on structured tasks (true/false and multiple choice), and Stage 2 fine-tunes on mixed open-ended data to improve generalization. Our 7B model achieves new state-of-the-art performance, improving overall accuracy to 52.93% (+3.59%) and open-ended accuracy to 14.83% while maintaining structured-task performance. It also achieves top semantic evaluation scores (Q-Score 6.24, P-Score 5.95), surpassing 32B models. These results demonstrate that PanoEnv-QA and our curriculum-based RL framework effectively instill 3D spatial intelligence in VLMs for omnidirectional perception.

Video-conditioned 4D shape generation aims to recover time-varying 3D geometry and view-consistent appearance directly from an input video. In this work, we introduce a native video-to-4D shape generation framework that synthesizes a single dynamic 3D representation end-to-end from the video. Our framework introduces three key components based on large-scale pre-trained 3D models: (i) a temporal attention that conditions generation on all frames while producing a time-indexed dynamic representation; (ii) a time-aware point sampling and 4D latent anchoring that promote temporally consistent geometry and texture; and (iii) noise sharing across frames to enhance temporal stability. Our method accurately captures non-rigid motion, volume changes, and even topological transitions without per-frame optimization. Across diverse in-the-wild videos, our method improves robustness and perceptual fidelity and reduces failure modes compared with the baselines.

Relighting is a crucial task with both practical demand and artistic value, and recent diffusion models have shown strong potential by enabling rich and controllable lighting effects. However, as they are typically optimized in semantic latent space, where proximity does not guarantee physical correctness in visual space, they often produce unrealistic results, such as overexposed highlights, misaligned shadows, and incorrect occlusions. We address this with UniLumos, a unified relighting framework for both images and videos that brings RGB-space geometry feedback into a flow matching backbone. By supervising the model with depth and normal maps extracted from its outputs, we explicitly align lighting effects with the scene structure, enhancing physical plausibility. Nevertheless, this feedback requires high-quality outputs for supervision in visual space, making standard multi-step denoising computationally expensive. To mitigate this, we employ path consistency learning, allowing supervision to remain effective even under few-step training regimes. To enable fine-grained relighting control and supervision, we design a structured six-dimensional annotation protocol capturing core illumination attributes. Building upon this, we propose LumosBench, a disentangled attribute-level benchmark that evaluates lighting controllability via large vision-language models, enabling automatic and interpretable assessment of relighting precision across individual dimensions. Extensive experiments demonstrate that UniLumos achieves state-of-the-art relighting quality with significantly improved physical consistency, while delivering a 20x speedup for both image and video relighting. Code is available at https://github.com/alibaba-damo-academy/Lumos-Custom.

Virtual try-on (VTON) aims to synthesize realistic images of a person wearing a target garment, with broad applications in e-commerce and digital fashion. While recent advances in latent diffusion models have substantially improved visual quality, existing approaches still struggle with preserving fine-grained garment details, achieving precise garment-body alignment, maintaining inference efficiency, and generalizing to diverse poses and clothing styles. To address these challenges, we propose DiffFit, a novel two-stage latent diffusion framework for high-fidelity virtual try-on. DiffFit adopts a progressive generation strategy: the first stage performs geometry-aware garment warping, aligning the garment with the target body through fine-grained deformation and pose adaptation. The second stage refines texture fidelity via a cross-modal conditional diffusion model that integrates the warped garment, the original garment appearance, and the target person image for high-quality rendering. By decoupling geometric alignment and appearance refinement, DiffFit effectively reduces task complexity and enhances both generation stability and visual realism. It excels in preserving garment-specific attributes such as textures, wrinkles, and lighting, while ensuring accurate alignment with the human body. Extensive experiments on large-scale VTON benchmarks demonstrate that DiffFit achieves superior performance over existing state-of-the-art methods in both quantitative metrics and perceptual evaluations.

Navigating unknown environments to find a target object is a significant challenge. While semantic information is crucial for navigation, relying solely on it for decision-making may not always be efficient, especially in environments with weak semantic cues. Additionally, many methods are susceptible to misdetections, especially in environments with visually similar objects. To address these limitations, we propose ApexNav, a zero-shot object navigation framework that is both more efficient and reliable. For efficiency, ApexNav adaptively utilizes semantic information by analyzing its distribution in the environment, guiding exploration through semantic reasoning when cues are strong, and switching to geometry-based exploration when they are weak. For reliability, we propose a target-centric semantic fusion method that preserves long-term memory of the target object and similar objects, reducing false detections and minimizing task failures. We evaluate ApexNav on the HM3Dv1, HM3Dv2, and MP3D datasets, where it outperforms state-of-the-art methods in both SR and SPL metrics. Comprehensive ablation studies further demonstrate the effectiveness of each module. Furthermore, real-world experiments validate the practicality of ApexNav in physical environments. Project page is available at https://robotics-star.com/ApexNav.

Recent advancements in Generalizable Gaussian Splatting have enabled robust 3D reconstruction from sparse input views by utilizing feed-forward Gaussian Splatting models, achieving superior cross-scene generalization. However, while many methods focus on geometric consistency, they often neglect the potential of text-driven guidance to enhance semantic understanding, which is crucial for accurately reconstructing fine-grained details in complex scenes. To address this limitation, we propose TextSplat--the first text-driven Generalizable Gaussian Splatting framework. By employing a text-guided fusion of diverse semantic cues, our framework learns robust cross-modal feature representations that improve the alignment of geometric and semantic information, producing high-fidelity 3D reconstructions. Specifically, our framework employs three parallel modules to obtain complementary representations: the Diffusion Prior Depth Estimator for accurate depth information, the Semantic Aware Segmentation Network for detailed semantic information, and the Multi-View Interaction Network for refined cross-view features. Then, in the Text-Guided Semantic Fusion Module, these representations are integrated via the text-guided and attention-based feature aggregation mechanism, resulting in enhanced 3D Gaussian parameters enriched with detailed semantic cues. Experimental results on various benchmark datasets demonstrate improved performance compared to existing methods across multiple evaluation metrics, validating the effectiveness of our framework. The code will be publicly available.

A significant gap exists between theory and practice in deep learning. Generalization and approximation error bounds are often derived for simplified models or are too loose to be informative. Many rely on the manifold hypothesis and on geometric regularity such as intrinsic dimension, curvature, and reach. Progress requires insight into data-manifold geometry and suitable benchmarks, yet existing options are polarized: analytic manifolds with known geometry but limited applicability, or real-world datasets where geometry is only coarsely estimable. We introduce a benchmarking framework for studying data geometry. We repurpose and extend dSprites and COIL-20 with additional transformation dimensions and dense, axis-aligned sampling, and pair them with finite-difference estimators that recover curvature, reach, and volume at near-ground-truth accuracy in a regime where general-purpose estimators are unreliable or difficult to deploy. The framework is intended as a controlled testbed, useful as a calibration environment for geometric estimators and a sandbox for probing theoretical assumptions. To illustrate its use, we present two application studies, namely assessing the scaling behavior of the bounds of Genovese et al. and Fefferman et al., and tracking the layer-wise geometry of a β-VAE, highlighting the behavior of current bounds and the value of controlled benchmarks for guiding and validating future theory. A reference implementation is available at https://github.com/koulakis/manifold-microscope.

Generating a street-level 3D scene from a single satellite image is a crucial yet challenging task. Current methods present a stark trade-off: geometry-colorization models achieve high geometric fidelity but are typically building-focused and lack semantic diversity. In contrast, proxy-based models use feed-forward image-to-3D frameworks to generate holistic scenes by jointly learning geometry and texture, a process that yields rich content but coarse and unstable geometry. We attribute these geometric failures to the extreme viewpoint gap and sparse, inconsistent supervision inherent in satellite-to-street data. We introduce Sat3DGen to address these fundamental challenges, which embodies a geometry-first methodology. This methodology enhances the feed-forward paradigm by integrating novel geometric constraints with a perspective-view training strategy, explicitly countering the primary sources of geometric error. This geometry-centric strategy yields a dramatic leap in both 3D accuracy and photorealism. For validation, we first constructed a new benchmark by pairing the VIGOR-OOD test set with high-resolution DSM data. On this benchmark, our method improves geometric RMSE from 6.76m to 5.20m. Crucially, this geometric leap also boosts photorealism, reducing the Fréchet Inception Distance (FID) from sim40 to 19 against the leading method, Sat2Density++, despite using no extra tailored image-quality modules. We demonstrate the versatility of our high-quality 3D assets through diverse downstream applications, including semantic-map-to-3D synthesis, multi-camera video generation, large-scale meshing, and unsupervised single-image Digital Surface Model (DSM) estimation. The code has been released on https://github.com/qianmingduowan/Sat3DGen.

Recent advances in language and vision have demonstrated that scaling up model capacity consistently improves performance across diverse tasks. In 3D visual geometry reconstruction, large-scale training has likewise proven effective for learning versatile representations. However, further scaling of 3D models is challenging due to the complexity of geometric supervision and the diversity of 3D data. To overcome these limitations, we propose MoRE, a dense 3D visual foundation model based on a Mixture-of-Experts (MoE) architecture that dynamically routes features to task-specific experts, allowing them to specialize in complementary data aspects and enhance both scalability and adaptability. Aiming to improve robustness under real-world conditions, MoRE incorporates a confidence-based depth refinement module that stabilizes and refines geometric estimation. In addition, it integrates dense semantic features with globally aligned 3D backbone representations for high-fidelity surface normal prediction. MoRE is further optimized with tailored loss functions to ensure robust learning across diverse inputs and multiple geometric tasks. Extensive experiments demonstrate that MoRE achieves state-of-the-art performance across multiple benchmarks and supports effective downstream applications without extra computation.

Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support. Generative models for 3D scenes, on the other hand, must rely on strong geometric priors to produce coherent outputs from sparse inputs. We bridge these two paradigms by performing flow matching directly in VGGT's latent space, leveraging its learned 3D priors without committing to any explicit downstream representation such as Gaussians, meshes, or video-VAE latents. This requires respecting the latent geometry: VGGT tokens occupy a product of high-dimensional hyperspheres on which standard Euclidean flow matching fails. We address this with a Riemannian Flow Matching framework defined on a product manifold of four hyperspheres, aligned with VGGT's multi-scale encoder, which keeps generated tokens on the valid data manifold required by the frozen decoding heads. On RealEstate10K, ScanNet++ and ETH3D, our method achieves strong performance against recent scene generation baselines in both per-view appearance and aggregated 3D geometry, establishing latent-space flow matching on geometric foundation models as a viable paradigm for 3D generation. The project page can be found https://lisaweijler.github.io/geometry-grounded-rfm/{here}.

Despite the availability of large-scale 3D datasets and advancements in 3D generative models, the complexity and uneven quality of 3D geometry and texture data continue to hinder the performance of 3D generation techniques. In most existing approaches, 3D geometry and texture are generated in separate stages using different models and non-unified representations, frequently leading to unsatisfactory coherence between geometry and texture. To address these challenges, we propose a novel framework for joint generation of 3D geometry and texture. Specifically, we focus in generate a versatile 2.5D representations that can be seamlessly transformed between 2D and 3D. Our approach begins by integrating multiview RGB, normal, and coordinate images into a unified representation, termed as 2.5D latents. Next, we adapt pre-trained 2D foundation models for high-fidelity 2.5D generation, utilizing both text and image conditions. Finally, we introduce a lightweight 2.5D-to-3D refiner-decoder framework that efficiently generates detailed 3D representations from 2.5D images. Extensive experiments demonstrate that our model not only excels in generating high-quality 3D objects with coherent structure and color from text and image inputs but also significantly outperforms existing methods in geometry-conditioned texture generation.

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

We present Image Sculpting, a new framework for editing 2D images by incorporating tools from 3D geometry and graphics. This approach differs markedly from existing methods, which are confined to 2D spaces and typically rely on textual instructions, leading to ambiguity and limited control. Image Sculpting converts 2D objects into 3D, enabling direct interaction with their 3D geometry. Post-editing, these objects are re-rendered into 2D, merging into the original image to produce high-fidelity results through a coarse-to-fine enhancement process. The framework supports precise, quantifiable, and physically-plausible editing options such as pose editing, rotation, translation, 3D composition, carving, and serial addition. It marks an initial step towards combining the creative freedom of generative models with the precision of graphics pipelines.

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.

Large language models have seen widespread adoption in math problem-solving. However, in geometry problems that usually require visual aids for better understanding, even the most advanced multi-modal models currently still face challenges in effectively using image information. High-quality data is crucial for enhancing the geometric capabilities of multi-modal models, yet existing open-source datasets and related efforts are either too challenging for direct model learning or suffer from misalignment between text and images. To overcome this issue, we introduce a novel pipeline that leverages GPT-4 and GPT-4V to generate relatively basic geometry problems with aligned text and images, facilitating model learning. We have produced a dataset of 4.9K geometry problems and combined it with 19K open-source data to form our GeoGPT4V dataset. Experimental results demonstrate that the GeoGPT4V dataset significantly improves the geometry performance of various models on the MathVista and MathVision benchmarks. The code is available at https://github.com/Lanyu0303/GeoGPT4V_Project

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.

Plane Geometry Diagram Synthesis has been a crucial task in computer graphics, with applications ranging from educational tools to AI-driven mathematical reasoning. Traditionally, we rely on manual tools (e.g., Matplotlib and GeoGebra) to generate precise diagrams, but this usually requires huge, complicated calculations. Recently, researchers start to work on model-based methods (e.g., Stable Diffusion and GPT5) to automatically generate diagrams, saving operational cost but usually suffering from limited realism and insufficient accuracy. In this paper, we propose a novel framework GeoSDF, to automatically generate diagrams efficiently and accurately with Signed Distance Field (SDF). Specifically, we first represent geometric elements (e.g., points, segments, and circles) in the SDF, then construct a series of constraint functions to represent geometric relationships. Next, we optimize those constructed constraint functions to get an optimized field of both elements and constraints. Finally, by rendering the optimized field, we can obtain the synthesized diagram. In our GeoSDF, we define a symbolic language to represent geometric elements and constraints, and our synthesized geometry diagrams can be self-verified in the SDF, ensuring both mathematical accuracy and visual plausibility. In experiments, through both qualitative and quantitative analysis, GeoSDF synthesized both normal high-school level and IMO-level geometry diagrams. We achieve 88.67\% synthesis accuracy by human evaluation in the IMO problem set. Furthermore, we obtain a very high accuracy of solving geometry problems (over 95\% while the current SOTA accuracy is around 75%) by leveraging our self-verification property. All of these demonstrate the advantage of GeoSDF, paving the way for more sophisticated, accurate, and flexible generation of geometric diagrams for a wide array of applications.

We present ABot-Earth 0.5, a generative 3D framework designed to synthesize vast, seamless 3D environments from ubiquitous, geospatially referenced satellite imagery. To achieve this, we propose a novel generative model formulated directly with the 3D Gaussian Splatting (3DGS) representation. The model is trained on a diverse corpus of existing real-world urban reconstructions, learning to generate realistic geometry and textures. At inference, it synthesizes novel 3D scenes conditioned solely on satellite imagery at a scalable rate of under 10 minutes per square kilometer, while demonstrating exceptional realism. The framework is designed for accessibility, with integrated hierarchical level-of-detail (LOD) structures that permit real-time, interactive visualization on web-based map engines. This high-fidelity simulation sandbox effectively mitigates the sim-to-real domain gap, enabling critical downstream Embodied AI applications like closed-loop UAV navigation. By providing an ultra-low-cost and high-efficiency solution, ABot-Earth 0.5 significantly lowers the technical and financial barriers to large-scale 3D reconstruction and empowers the future of global digital earth visualization.

Geometric foundation models show promise in 3D reconstruction, yet their progress is severely constrained by the scarcity of diverse, large-scale 3D annotations. While Internet videos offer virtually unlimited raw data, utilizing them as a scaling source for geometric learning is challenging due to the absence of ground-truth geometry and the presence of observational noise. To address this, we propose SAGE, a framework for Scalable Adaptation of GEometric foundation models from raw video streams. SAGE leverages a hierarchical mining pipeline to transform videos into training trajectories and hybrid supervision: (1) Informative training trajectory selection; (2) Sparse Geometric Anchoring via SfM point clouds for global structural guidance; and (3) Dense Differentiable Consistency via 3D Gaussian rendering for multi-view constraints. To prevent catastrophic forgetting, we introduce a regularization strategy using anchor data. Extensive experiments show that SAGE significantly enhances zero-shot generalization, reducing Chamfer Distance by 20-42% on unseen benchmarks (7Scenes, TUM-RGBD, Matterport3D) compared to state-of-the-art baselines. To our knowledge, SAGE pioneers the adaptation of geometric foundation models via Internet video, establishing a scalable paradigm for general-purpose 3D learning.

Recent 3D geometric foundation models, such as VGGT, provide robust feed-forward 3D reconstruction by directly predicting camera poses and 3D scene points from input images. However, their results remain inaccurate, and scaling them to long sequences or large unordered image sets typically requires chunk-wise processing, which can introduce drift and inconsistency. We present Glob3R, a global SfM-style reconstruction built on 3D foundation models. Our key idea is to explicitly optimize feed-forward geometric predictions. To this end, we augment a frozen Pi3X backbone with a lightweight dense matching head that predicts image warps between selected reference frames and neighboring views. These dense warps are converted into sparse but reliable multi-view feature tracks, which provide correspondence constraints for global optimization. We further introduce a keyframe-based sliding-window association strategy that propagates tracks and relative poses across overlapping windows, enabling scalable reconstruction. Finally, we perform global motion averaging and bundle adjustment to refine camera poses, reduce scale inconsistencies, and recover dense scene geometry. Extensive experiments on indoor, outdoor, large-scale driving, and unordered SfM benchmarks demonstrate that Glob3R achieves robust and accurate reconstruction. It consistently improves over feed-forward foundation-model baselines and recent scalable reconstruction methods, while being more robust than classical SfM pipelines. The refined poses also lead to higher-quality neural rendering, validating the benefit of combining foundation-model priors with global geometric optimization. Project page: https://junyuandeng.github.io/Glob3r

Text-to-3D generation represents an exciting field that has seen rapid advancements, facilitating the transformation of textual descriptions into detailed 3D models. However, current progress often neglects the intricate high-order correlation of geometry and texture within 3D objects, leading to challenges such as over-smoothness, over-saturation and the Janus problem. In this work, we propose a method named ``3D Gaussian Generation via Hypergraph (Hyper-3DG)'', designed to capture the sophisticated high-order correlations present within 3D objects. Our framework is anchored by a well-established mainflow and an essential module, named ``Geometry and Texture Hypergraph Refiner (HGRefiner)''. This module not only refines the representation of 3D Gaussians but also accelerates the update process of these 3D Gaussians by conducting the Patch-3DGS Hypergraph Learning on both explicit attributes and latent visual features. Our framework allows for the production of finely generated 3D objects within a cohesive optimization, effectively circumventing degradation. Extensive experimentation has shown that our proposed method significantly enhances the quality of 3D generation while incurring no additional computational overhead for the underlying framework. (Project code: https://github.com/yjhboy/Hyper3DG)

In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles. Local approximations obtained by local PCAs are collected into a rank k tangent subbundle on R^d, k<d, which we call a principal subbundle. This determines a sub-Riemannian metric on R^d. We show that sub-Riemannian geodesics with respect to this metric can successfully be applied to a number of important problems, such as: explicit construction of an approximating submanifold M, construction of a representation of the point-cloud in R^k, and computation of distances between observations, taking the learned geometry into account. The reconstruction is guaranteed to equal the true submanifold in the limit case where tangent spaces are estimated exactly. Via simulations, we show that the framework is robust when applied to noisy data. Furthermore, the framework generalizes to observations on an a priori known Riemannian manifold.

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/.

Recent advancements in neural visual geometry, including transformer-based models such as VGGT and Pi3, have achieved impressive accuracy on 3D reconstruction tasks. However, their reliance on full attention makes them fundamentally limited by GPU memory capacity, preventing them from scaling to large, unordered image collections. We introduce MERG3R, a training-free divide-and-conquer framework that enables geometric foundation models to operate far beyond their native memory limits. MERG3R first reorders and partitions unordered images into overlapping, geometrically diverse subsets that can be reconstructed independently. It then merges the resulting local reconstructions through an efficient global alignment and confidence-weighted bundle adjustment procedure, producing a globally consistent 3D model. Our framework is model-agnostic and can be paired with existing neural geometry models. Across large-scale datasets, including 7-Scenes, NRGBD, Tanks & Temples, and Cambridge Landmarks, MERG3R consistently improves reconstruction accuracy, memory efficiency, and scalability, enabling high-quality reconstruction when the dataset exceeds memory capacity limits.

Recent advances in 3D Gaussian Splatting (3DGS) have enabled real-time, photorealistic scene reconstruction. However, conventional 3DGS frameworks typically rely on sparse point clouds derived from Structure-from-Motion (SfM), which inherently suffer from scale ambiguity, limited geometric consistency, and strong view dependency due to the lack of geometric priors. In this work, a LiDAR-centric 3D Gaussian Splatting framework is proposed that explicitly incorporates metric geometric priors into the entire Gaussian optimization process. Instead of treating LiDAR data as a passive initialization source, 3DGS optimization is reformulated as a geometry-conditioned allocation and refinement problem under a fixed representational budget. Specifically, this work introduces (i) a geometry-texture-aware allocation strategy that selectively assigns Gaussian primitives to regions with high structural or appearance complexity, (ii) a curvature-adaptive refinement mechanism that dynamically guides Gaussian splitting toward geometrically complex areas during training, and (iii) a confidence-aware metric depth regularization that anchors the reconstructed geometry to absolute scale using LiDAR measurements while maintaining optimization stability. Extensive experiments on the ScanNet++ dataset and a custom real-world dataset validate the proposed approach. The results demonstrate state-of-the-art performance in metric-scale reconstruction with high geometric fidelity.

Existing Large Multimodal Models (LMMs) struggle with mathematical geometric reasoning due to a lack of high-quality image-text paired data. Current geometric data generation approaches, which apply preset templates to generate geometric data or use Large Language Models (LLMs) to rephrase questions and answers (Q&A), unavoidably limit data accuracy and diversity. To synthesize higher-quality data, we propose a two-stage Reverse Chain-of-Thought (R-CoT) geometry problem generation pipeline. First, we introduce GeoChain to produce high-fidelity geometric images and corresponding descriptions highlighting relations among geometric elements. We then design a Reverse A&Q method that reasons step-by-step based on the descriptions and generates questions in reverse from the reasoning results. Experiments demonstrate that the proposed method brings significant and consistent improvements on multiple LMM baselines, achieving new performance records in the 2B, 7B, and 8B settings. Notably, R-CoT-8B significantly outperforms previous state-of-the-art open-source mathematical models by 16.6% on MathVista and 9.2% on GeoQA, while also surpassing the closed-source model GPT-4o by an average of 13% across both datasets. The code is available at https://github.com/dle666/R-CoT.

This paper introduces LaS-Comp, a zero-shot and category-agnostic approach that leverages the rich geometric priors of 3D foundation models to enable 3D shape completion across diverse types of partial observations. Our contributions are threefold: First, harnesses these powerful generative priors for completion through a complementary two-stage design: (i) an explicit replacement stage that preserves the partial observation geometry to ensure faithful completion; and (ii) an implicit refinement stage ensures seamless boundaries between the observed and synthesized regions. Second, our framework is training-free and compatible with different 3D foundation models. Third, we introduce Omni-Comp, a comprehensive benchmark combining real-world and synthetic data with diverse and challenging partial patterns, enabling a more thorough and realistic evaluation. Both quantitative and qualitative experiments demonstrate that our approach outperforms previous state-of-the-art approaches. Our code and data will be available at https://github.com/DavidYan2001/LaS-Comp{LaS-Comp}.

Automatic generation of computer-aided design (CAD) models is a core technology for enabling intelligence in advanced manufacturing. Existing generation methods based on large language models (LLMs) often fall short when handling complex CAD models characterized by long operation sequences, diverse operation types, and strong geometric constraints, primarily because reasoning chains break and effective error-correction mechanisms are lacking. To address this problem, this paper proposes a memory-augmented reinforcement learning framework for CAD generation agents. The framework encapsulates the underlying geometric kernel into a structured toolchain callable by the agent and builds a closed-loop mechanism of design intent understanding, global planning, execution, and multi-dimensional verification. It also designs a dual-track memory module consisting of a case library and a skill library, and proposes a dynamic utility retrieval algorithm. By introducing reinforcement learning into retrieval and policy optimization, the agent can effectively avoid retrieval traps in which examples are semantically similar but geometrically infeasible, enabling online self-correction and continual evolution without additional large-scale annotated data. Experiments show that the proposed method significantly improves both the success rate and geometric consistency on complex CAD model generation tasks.

3D cellular image segmentation methods are commonly divided into non-2D-based and 2D-based approaches, the latter reconstructing 3D shapes from the segmentation results of 2D layers. However, errors in 2D results often propagate, leading to oversegmentations in the final 3D results. To tackle this issue, we introduce an interpretable geometric framework that addresses the oversegmentations by correcting the 2D segmentation results based on geometric information from adjacent layers. Leveraging both geometric (layer-to-layer, 2D) and topological (3D shape) features, we use binary classification to determine whether neighboring cells should be stitched. We develop a pre-trained classifier on public plant cell datasets and validate its performance on animal cell datasets, confirming its effectiveness in correcting oversegmentations under the transfer learning setting. Furthermore, we demonstrate that our framework can be extended to correcting oversegmentation on non-2D-based methods. A clear pipeline is provided for end-users to build the pre-trained model to any labeled dataset.

Emerging 3D geometric foundation models, such as DUSt3R, offer a promising approach for in-the-wild 3D vision tasks. However, due to the high-dimensional nature of the problem space and scarcity of high-quality 3D data, these pre-trained models still struggle to generalize to many challenging circumstances, such as limited view overlap or low lighting. To address this, we propose LoRA3D, an efficient self-calibration pipeline to specialize the pre-trained models to target scenes using their own multi-view predictions. Taking sparse RGB images as input, we leverage robust optimization techniques to refine multi-view predictions and align them into a global coordinate frame. In particular, we incorporate prediction confidence into the geometric optimization process, automatically re-weighting the confidence to better reflect point estimation accuracy. We use the calibrated confidence to generate high-quality pseudo labels for the calibrating views and use low-rank adaptation (LoRA) to fine-tune the models on the pseudo-labeled data. Our method does not require any external priors or manual labels. It completes the self-calibration process on a single standard GPU within just 5 minutes. Each low-rank adapter requires only 18MB of storage. We evaluated our method on more than 160 scenes from the Replica, TUM and Waymo Open datasets, achieving up to 88% performance improvement on 3D reconstruction, multi-view pose estimation and novel-view rendering.

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.

This report presents a comprehensive framework for generating high-quality 3D shapes and textures from diverse input prompts, including single images, multi-view images, and text descriptions. The framework consists of 3D shape generation and texture generation. (1). The 3D shape generation pipeline employs a Variational Autoencoder (VAE) to encode implicit 3D geometries into a latent space and a diffusion network to generate latents conditioned on input prompts, with modifications to enhance model capacity. An alternative Artist-Created Mesh (AM) generation approach is also explored, yielding promising results for simpler geometries. (2). Texture generation involves a multi-stage process starting with frontal images generation followed by multi-view images generation, RGB-to-PBR texture conversion, and high-resolution multi-view texture refinement. A consistency scheduler is plugged into every stage, to enforce pixel-wise consistency among multi-view textures during inference, ensuring seamless integration. The pipeline demonstrates effective handling of diverse input formats, leveraging advanced neural architectures and novel methodologies to produce high-quality 3D content. This report details the system architecture, experimental results, and potential future directions to improve and expand the framework. The source code and pretrained weights are released at: https://github.com/Tencent/Tencent-XR-3DGen.

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.

Incorporating spatial information, particularly those influenced by climate, weather, and demographic factors, is crucial for improving underwriting precision and enhancing risk management in insurance. However, spatial data are often unstructured, high-dimensional, and difficult to integrate into predictive models. Embedding methods are needed to convert spatial data into meaningful representations for modelling tasks. We propose a novel multi-view contrastive learning framework for generating spatial embeddings that combine information from multiple spatial data sources. To train the model, we construct a spatial dataset that merges satellite imagery and OpenStreetMap features across Europe. The framework aligns these spatial views with coordinate-based encodings, producing low-dimensional embeddings that capture both spatial structure and contextual similarity. Once trained, the model generates embeddings directly from latitude-longitude pairs, enabling any dataset with coordinates to be enriched with meaningful spatial features without requiring access to the original spatial inputs. In a case study on French real estate prices, we compare models trained on raw coordinates against those using our spatial embeddings as inputs. The embeddings consistently improve predictive accuracy across generalised linear, additive, and boosting models, while providing interpretable spatial effects and demonstrating transferability to unseen regions.

Data-driven engineering design is constrained by the lack of large-scale 3D datasets that pair geometry with physics-based performance labels. In particular, existing 3D data augmentation techniques have limitations in preserving subtle and diverse geometric variations, and it remains difficult to automate the subsequent simulation-labeling process, where boundary conditions vary depending on the generated geometry. We present DeepJEB++, a foundation-model-driven data-augmentation framework that expands a small seed set of jet engine brackets into a large, simulation-labeled 3D dataset under constrained resources. Our key idea is to augment in the data-rich 2D latent space, then transfer to 3D. In Stage 1, we fine-tune a pretrained 2D latent diffusion model on multi-view renders and synthesize novel views by latent interpolation, retaining manufacturable designs through a vision-language-model (VLM) quality filter. In Stage 2, the validated images are lifted to 3D meshes by a domain-adapted generative foundation model. In Stage 3, an automated pipeline recognizes the load and bolt interfaces on each mesh and assigns finite-element labels -- mass, stress, and displacement -- without manual intervention. We assess augmentation quality along three intrinsic axes: manufacturability, label fidelity against the SimJEB ground truth, and distributional consistency. Starting from fewer than 400 seed designs, DeepJEB++ yields 15,360 simulation-labeled 3D brackets -- a 40x expansion -- using a single GPU per stage. The dataset will be made publicly available to support reproducible engineering-AI research.

Recent advances in data-driven geometric multi-view 3D reconstruction foundation models (e.g., DUSt3R) have shown remarkable performance across various 3D vision tasks, facilitated by the release of large-scale, high-quality 3D datasets. However, as we observed, constrained by their matching-based principles, the reconstruction quality of existing models suffers significant degradation in challenging regions with limited matching cues, particularly in weakly textured areas and low-light conditions. To mitigate these limitations, we propose to harness the inherent robustness of monocular geometry estimation to compensate for the inherent shortcomings of matching-based methods. Specifically, we introduce a monocular-guided refinement module that integrates monocular geometric priors into multi-view reconstruction frameworks. This integration substantially enhances the robustness of multi-view reconstruction systems, leading to high-quality feed-forward reconstructions. Comprehensive experiments across multiple benchmarks demonstrate that our method achieves substantial improvements in both mutli-view camera pose estimation and point cloud accuracy.

In this report, we introduce UltraShape 1.0, a scalable 3D diffusion framework for high-fidelity 3D geometry generation. The proposed approach adopts a two-stage generation pipeline: a coarse global structure is first synthesized and then refined to produce detailed, high-quality geometry. To support reliable 3D generation, we develop a comprehensive data processing pipeline that includes a novel watertight processing method and high-quality data filtering. This pipeline improves the geometric quality of publicly available 3D datasets by removing low-quality samples, filling holes, and thickening thin structures, while preserving fine-grained geometric details. To enable fine-grained geometry refinement, we decouple spatial localization from geometric detail synthesis in the diffusion process. We achieve this by performing voxel-based refinement at fixed spatial locations, where voxel queries derived from coarse geometry provide explicit positional anchors encoded via RoPE, allowing the diffusion model to focus on synthesizing local geometric details within a reduced, structured solution space. Our model is trained exclusively on publicly available 3D datasets, achieving strong geometric quality despite limited training resources. Extensive evaluations demonstrate that UltraShape 1.0 performs competitively with existing open-source methods in both data processing quality and geometry generation. All code and trained models will be released to support future research.

Generative models have achieved remarkable progress, yet applying them to satellite imagery remains challenging. Unlike natural imagery, satellite scenes are structured by spatially complex and semantically distinct geometries. Prior work addresses this complexity by adapting natural image frameworks using dense rasters or sparse prompts, trading off annotation cost and fidelity while breaking compatibility with vector primitives commonly used to represent geographic information. We introduce TerraDiT-Ω, a unified spatial control framework that generates satellite imagery directly from any native geospatial primitive. By jointly leveraging precise annotations (polygons, polylines) and coarser ones (bounding boxes, points), the model supports controllable layouts across varying annotation budgets, broadening applicability to design tasks such as urban planning while remaining naturally compatible with end-to-end GeoAI workflows. To effectively leverage these primitives during generation, we propose Geometry-Aware Local Attention, a conditioning mechanism that injects explicit geometric cues into the attention space. Across all conditioning formats, our approach consistently outperforms both dense-control and sparse-control baselines. Furthermore, this flexibility enables controllable synthetic data augmentation using a single generative model, improving downstream performance on land-cover segmentation, object detection, road graph extraction, and scene classification. Code, data, and weights are available at https://github.com/mvrl/TerraDiT.

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

Recovering high-fidelity 3D hand geometry from images is a critical task in computer vision, holding significant value for domains such as robotics, animation and VR/AR. Crucially, scalable applications demand both accuracy and deployment flexibility, requiring the ability to leverage massive amounts of unstructured image data from the internet or enable deployment on consumer-grade RGB cameras without complex calibration. However, current methods face a dilemma. While single-view approaches are easy to deploy, they suffer from depth ambiguity and occlusion. Conversely, multi-view systems resolve these uncertainties but typically demand fixed, calibrated setups, limiting their real-world utility. To bridge this gap, we draw inspiration from 3D foundation models that learn explicit geometry directly from visual data. By reformulating hand reconstruction from arbitrary views as a visual-geometry grounded task, we propose a feed-forward architecture that, for the first time in literature, jointly infers 3D hand meshes and camera poses from uncalibrated views. Extensive evaluations show that our approach outperforms state-of-the-art benchmarks and demonstrates strong generalization to uncalibrated, in-the-wild scenarios. Here is the link of our project page: https://lym29.github.io/HGGT/.

Generating high-quality 3D objects from textual descriptions remains a challenging problem due to computational cost, the scarcity of 3D data, and complex 3D representations. We introduce Geometry Image Diffusion (GIMDiffusion), a novel Text-to-3D model that utilizes geometry images to efficiently represent 3D shapes using 2D images, thereby avoiding the need for complex 3D-aware architectures. By integrating a Collaborative Control mechanism, we exploit the rich 2D priors of existing Text-to-Image models such as Stable Diffusion. This enables strong generalization even with limited 3D training data (allowing us to use only high-quality training data) as well as retaining compatibility with guidance techniques such as IPAdapter. In short, GIMDiffusion enables the generation of 3D assets at speeds comparable to current Text-to-Image models. The generated objects consist of semantically meaningful, separate parts and include internal structures, enhancing both usability and versatility.

Generating executable CAD programs from images requires alignment between visual geometry and symbolic program representations, a capability that current methods fail to learn reliably as design complexity increases. Existing fine-tuning approaches rely on either limited supervised datasets or expensive post-training pipelines, resulting in brittle systems that restrict progress in generative CAD design. We argue that the primary bottleneck lies not in model or algorithmic capacity, but in the scarcity of diverse training examples that align visual geometry with program syntax. This limitation is especially acute because the collection of diverse and verified engineering datasets is both expensive and difficult to scale, constraining the development of robust generative CAD models. We introduce Geometric Inference Feedback Tuning (GIFT), a data augmentation framework that leverages geometric feedback to turn test-time compute into a bootstrapped set of high-quality training samples. GIFT combines two mechanisms: Soft-Rejection Sampling (GIFT-REJECT), which retains diverse high-fidelity programs beyond exact ground-truth matches, and Failure-Driven Augmentation (GIFT-FAIL), which converts near-miss predictions into synthetic training examples that improve robustness on challenging geometries. By amortizing inference-time search into the model parameters, GIFT captures the benefits of test-time scaling while reducing inference compute by 80%. It improves mean IoU by 12% over a strong supervised baseline and remains competitive with more complex multimodal systems, without requiring additional human annotation or specialized architectures.

A triangular mesh is one of the most popular 3D data representations. As such, the deployment of deep neural networks for mesh processing is widely spread and is increasingly attracting more attention. However, neural networks are prone to adversarial attacks, where carefully crafted inputs impair the model's functionality. The need to explore these vulnerabilities is a fundamental factor in the future development of 3D-based applications. Recently, mesh attacks were studied on the semantic level, where classifiers are misled to produce wrong predictions. Nevertheless, mesh surfaces possess complex geometric attributes beyond their semantic meaning, and their analysis often includes the need to encode and reconstruct the geometry of the shape. We propose a novel framework for a geometric adversarial attack on a 3D mesh autoencoder. In this setting, an adversarial input mesh deceives the autoencoder by forcing it to reconstruct a different geometric shape at its output. The malicious input is produced by perturbing a clean shape in the spectral domain. Our method leverages the spectral decomposition of the mesh along with additional mesh-related properties to obtain visually credible results that consider the delicacy of surface distortions. Our code is publicly available at https://github.com/StolikTomer/SAGA.

Geometric spatial reasoning forms the foundation of many applications in artificial intelligence, yet the ability of large language models (LLMs) to operate over geometric spatial information expressed in procedural code remains underexplored. In this paper, we address this gap by formalizing the Program-to-Geometry task, which challenges models to translate programmatic drawing code into accurate and abstract geometric reasoning. To evaluate this capability, we present GeoGramBench, a benchmark of 500 carefully refined problems organized by a tailored three-level taxonomy that considers geometric complexity rather than traditional mathematical reasoning complexity. Our comprehensive evaluation of 17 frontier LLMs reveals consistent and pronounced deficiencies: even the most advanced models achieve less than 50% accuracy at the highest abstraction level. These results highlight the unique challenges posed by program-driven spatial reasoning and establish GeoGramBench as a valuable resource for advancing research in symbolic-to-spatial geometric reasoning. Project page: https://github.com/LiAuto-DSR/GeoGramBench.

Towards intelligent image editing, object removal should eliminate both the target object and its causal visual artifacts, such as shadows and reflections. However, existing image appearance-based methods either follow strictly mask-aligned training and fail to remove these causal effects which are not explicitly masked, or adopt loosely mask-aligned strategies that lack controllability and may unintentionally over-erase other objects. We identify that these limitations stem from ignoring the causal relationship between an object's geometry presence and its visual effects. To address this limitation, we propose a geometry-aware two-stage framework that decouples object removal into (1) geometry removal and (2) appearance rendering. In the first stage, we remove the object directly from the geometry (e.g., depth) using strictly mask-aligned supervision, enabling structure-aware editing with strong geometric constraints. In the second stage, we render a photorealistic RGB image conditioned on the updated geometry, where causal visual effects are considered implicitly as a result of the modified 3D geometry. To guide learning in the geometry removal stage, we introduce a preference-driven objective based on positive and negative sample pairs, encouraging the model to remove objects as well as their causal visual artifacts while avoiding new structural insertions. Extensive experiments demonstrate that our method achieves state-of-the-art performance in removing both objects and their associated artifacts on two popular benchmarks. The code is available at https://github.com/buxiangzhiren/GeoRemover.

3D vision foundation models like Visual Geometry Grounded Transformer (VGGT) have advanced greatly in geometric perception. However, it is time-consuming and memory-intensive for long sequences, limiting application to large-scale scenes beyond hundreds of images. To address this, we propose LiteVGGT, achieving up to 10x speedup and substantial memory reduction, enabling efficient processing of 1000-image scenes. We derive two key insights for 3D reconstruction: (1) tokens from local image regions have inherent geometric correlations, leading to high similarity and computational redundancy; (2) token similarity across adjacent network layers remains stable, allowing for reusable merge decisions. Guided by these, we design a simple yet efficient strategy, dubbed geometry-aware cached token merging. We analyze each token's geometric importance, optimizing anchor token selection to better preserve key information for reconstruction. We also cache and reuse merge indices across layers, substantially reducing latency with minimal accuracy impact. This strategy retains VGGT's core performance, enabling efficient fine-tuning and FP8 quantization for further gains. Extensive experiments validate LiteVGGT's effectiveness, scalability, and robustness. Project page: https://garlicba.github.io/LiteVGGT/

6D object pose estimation, which predicts the transformation of an object relative to the camera, remains challenging for unseen objects. Existing approaches typically rely on explicitly constructing feature correspondences between the query image and either the object model or template images. In this work, we propose PoseGAM, a geometry-aware multi-view framework that directly predicts object pose from a query image and multiple template images, eliminating the need for explicit matching. Built upon recent multi-view-based foundation model architectures, the method integrates object geometry information through two complementary mechanisms: explicit point-based geometry and learned features from geometry representation networks. In addition, we construct a large-scale synthetic dataset containing more than 190k objects under diverse environmental conditions to enhance robustness and generalization. Extensive evaluations across multiple benchmarks demonstrate our state-of-the-art performance, yielding an average AR improvement of 5.1% over prior methods and achieving up to 17.6% gains on individual datasets, indicating strong generalization to unseen objects. Project page: https://windvchen.github.io/PoseGAM/ .

We introduce a diffusion-based framework that performs aligned novel view image and geometry generation via a warping-and-inpainting methodology. Unlike prior methods that require dense posed images or pose-embedded generative models limited to in-domain views, our method leverages off-the-shelf geometry predictors to predict partial geometries viewed from reference images, and formulates novel-view synthesis as an inpainting task for both image and geometry. To ensure accurate alignment between generated images and geometry, we propose cross-modal attention distillation, where attention maps from the image diffusion branch are injected into a parallel geometry diffusion branch during both training and inference. This multi-task approach achieves synergistic effects, facilitating geometrically robust image synthesis as well as well-defined geometry prediction. We further introduce proximity-based mesh conditioning to integrate depth and normal cues, interpolating between point cloud and filtering erroneously predicted geometry from influencing the generation process. Empirically, our method achieves high-fidelity extrapolative view synthesis on both image and geometry across a range of unseen scenes, delivers competitive reconstruction quality under interpolation settings, and produces geometrically aligned colored point clouds for comprehensive 3D completion. Project page is available at https://cvlab-kaist.github.io/MoAI.

Previous works that leverage video models for image-to-3D scene generation often suffer from geometric distortions and blurry content. Using video generation models to implicitly maintain geometric consistency according to a single-frame input is ineffective. In this paper, we present a two-stage method, named GeoWorld, that renovates the image-to-3D scene generation pipeline by providing full-frame geometry features. The first-stage video generation model, followed by a multi-view geometry model, produces full-frame geometry features, which are then used as a mental draft of geometric conditions to aid the second-stage video-generation model. A geometric loss is proposed to impose real-world geometric constraints, and a geometry adaptation module is introduced to ensure the effective utilization of geometry features. Thanks to full-frame geometric modeling, the two smaller video models in our two-stage method can generate higher-fidelity 3D scenes than SOTA methods, while being even faster, e.g. 7.5times faster than Hunyuan-Voyager. Project page: https://peaes.github.io/GeoWorld.

Despite the remarkable developments achieved by recent 3D generation works, scaling these methods to geographic extents, such as modeling thousands of square kilometers of Earth's surface, remains an open challenge. We address this through a dual innovation in data infrastructure and model architecture. First, we introduce Aerial-Earth3D, the largest 3D aerial dataset to date, consisting of 50k curated scenes (each measuring 600m x 600m) captured across the U.S. mainland, comprising 45M multi-view Google Earth frames. Each scene provides pose-annotated multi-view images, depth maps, normals, semantic segmentation, and camera poses, with explicit quality control to ensure terrain diversity. Building on this foundation, we propose EarthCrafter, a tailored framework for large-scale 3D Earth generation via sparse-decoupled latent diffusion. Our architecture separates structural and textural generation: 1) Dual sparse 3D-VAEs compress high-resolution geometric voxels and textural 2D Gaussian Splats (2DGS) into compact latent spaces, largely alleviating the costly computation suffering from vast geographic scales while preserving critical information. 2) We propose condition-aware flow matching models trained on mixed inputs (semantics, images, or neither) to flexibly model latent geometry and texture features independently. Extensive experiments demonstrate that EarthCrafter performs substantially better in extremely large-scale generation. The framework further supports versatile applications, from semantic-guided urban layout generation to unconditional terrain synthesis, while maintaining geographic plausibility through our rich data priors from Aerial-Earth3D. Our project page is available at https://whiteinblue.github.io/earthcrafter/

Large Multimodal Models (LMMs) often struggle with geometric reasoning due to visual hallucinations and a lack of mathematically precise Chain-of-Thought (CoT) data. To address this, we propose the GeoSym Engine, an automated and scalable neuro-symbolic framework. By leveraging a type-conditional grammar and an analytic SymGT Solver, it derives exact symbolic ground truths and seamlessly integrates with a robust rendering pipeline to produce high-precision geometric diagrams. Using this engine, we construct GeoSym127K, a difficulty-stratified dataset featuring 51K high-resolution images, 127K questions with symbolic ground truths, and 55K answer-verified CoT QA pairs. We also introduce GeoSym-Bench, an expert-curated suite of 511 complex samples for rigorous evaluation. Through extensive supervised fine-tuning (SFT), we demonstrate that GeoSym drives concentrated improvements specifically on diagram-dependent and multi-step geometry tasks. Our Qwen3-VL-8B model gains an absolute +22.21% on the MathVerse Vision-Only subset and reaches 61.52% (+6.19% improvement) on WeMath, mitigating long-horizon logic fragmentation and outperforming advanced closed-source models like Doubao-1.8. Furthermore, applying Reinforcement Learning with Verifiable Rewards (RLVR) via GRPO reveals that initializing from structural SFT checkpoints substantially elevates the performance ceiling over zero-shot RL. Driven by deterministic exact-match signals, this showcases the robust scaling potential of our verifiable reasoning synthesis. Datasets and code are available at https://huggingface.co/datasets/Tomie0506/GeoSym127K and https://github.com/Tomie56/GeoSym127K.

In this paper, we propose Img2CAD, the first approach to our knowledge that uses 2D image inputs to generate CAD models with editable parameters. Unlike existing AI methods for 3D model generation using text or image inputs often rely on mesh-based representations, which are incompatible with CAD tools and lack editability and fine control, Img2CAD enables seamless integration between AI-based 3D reconstruction and CAD software. We have identified an innovative intermediate representation called Structured Visual Geometry (SVG), characterized by vectorized wireframes extracted from objects. This representation significantly enhances the performance of generating conditioned CAD models. Additionally, we introduce two new datasets to further support research in this area: ABC-mono, the largest known dataset comprising over 200,000 3D CAD models with rendered images, and KOCAD, the first dataset featuring real-world captured objects alongside their ground truth CAD models, supporting further research in conditioned CAD model generation.

We present a novel generative 3D modeling system, coined CraftsMan, which can generate high-fidelity 3D geometries with highly varied shapes, regular mesh topologies, and detailed surfaces, and, notably, allows for refining the geometry in an interactive manner. Despite the significant advancements in 3D generation, existing methods still struggle with lengthy optimization processes, irregular mesh topologies, noisy surfaces, and difficulties in accommodating user edits, consequently impeding their widespread adoption and implementation in 3D modeling software. Our work is inspired by the craftsman, who usually roughs out the holistic figure of the work first and elaborates the surface details subsequently. Specifically, we employ a 3D native diffusion model, which operates on latent space learned from latent set-based 3D representations, to generate coarse geometries with regular mesh topology in seconds. In particular, this process takes as input a text prompt or a reference image and leverages a powerful multi-view (MV) diffusion model to generate multiple views of the coarse geometry, which are fed into our MV-conditioned 3D diffusion model for generating the 3D geometry, significantly improving robustness and generalizability. Following that, a normal-based geometry refiner is used to significantly enhance the surface details. This refinement can be performed automatically, or interactively with user-supplied edits. Extensive experiments demonstrate that our method achieves high efficacy in producing superior-quality 3D assets compared to existing methods. HomePage: https://craftsman3d.github.io/, Code: https://github.com/wyysf-98/CraftsMan

Mathematical geometric reasoning is essential for scientific discovery and educational development, requiring precise logic and rigorous formal verification. While recent advances in Multimodal Large Language Models (MLLMs) have improved reasoning tasks, existing models typically struggle with formal geometric reasoning, particularly when dynamically constructing and verifying auxiliary geometric elements. To address these challenges, we introduce Geoint-R1, a multimodal reasoning framework designed to generate formally verifiable geometric solutions from textual descriptions and visual diagrams. Geoint-R1 uniquely integrates auxiliary elements construction, formal reasoning represented via Lean4, and interactive visualization. To systematically evaluate and advance formal geometric reasoning, we propose the Geoint benchmark, comprising 1,885 rigorously annotated geometry problems across diverse topics such as plane, spatial, and solid geometry. Each problem includes structured textual annotations, precise Lean4 code for auxiliary constructions, and detailed solution steps verified by experts. Extensive experiments demonstrate that Geoint-R1 significantly surpasses existing multimodal and math-specific reasoning models, particularly on challenging problems requiring explicit auxiliary element constructions.

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.

Realistic video simulation has shown significant potential across diverse applications, from virtual reality to film production. This is particularly true for scenarios where capturing videos in real-world settings is either impractical or expensive. Existing approaches in video simulation often fail to accurately model the lighting environment, represent the object geometry, or achieve high levels of photorealism. In this paper, we propose Anything in Any Scene, a novel and generic framework for realistic video simulation that seamlessly inserts any object into an existing dynamic video with a strong emphasis on physical realism. Our proposed general framework encompasses three key processes: 1) integrating a realistic object into a given scene video with proper placement to ensure geometric realism; 2) estimating the sky and environmental lighting distribution and simulating realistic shadows to enhance the light realism; 3) employing a style transfer network that refines the final video output to maximize photorealism. We experimentally demonstrate that Anything in Any Scene framework produces simulated videos of great geometric realism, lighting realism, and photorealism. By significantly mitigating the challenges associated with video data generation, our framework offers an efficient and cost-effective solution for acquiring high-quality videos. Furthermore, its applications extend well beyond video data augmentation, showing promising potential in virtual reality, video editing, and various other video-centric applications. Please check our project website https://anythinginanyscene.github.io for access to our project code and more high-resolution video results.

Recent advances in generative models highlight the power of geometry-aware modeling in manifold-constrained settings. Yet, for natural images, the field remains confined to Euclidean assumptions, failing to exploit the potential of intrinsic geometric structures within the data. In this work, we investigate the geometry of natural images and observe that semantic information is predominantly encoded in directional components, while norm components can be approximated by the global average. This property holds across both RGB and latent spaces, suggesting that natural images can be effectively modeled on a hypersphere. Building on this finding, we introduce Spherical Optimal Transport Flow Matching (SOT-CFM), which utilizes angular distance, and Spherical Flow Matching (SFM), which constrains dynamics directly on the manifold. Our experiments demonstrate that these geometry-aware methods achieve superior performance against Euclidean baselines. Ultimately, this work provides a novel perspective that bridges the gap between Riemannian manifold-based modeling and natural image generation.

Reconstructing 3D representations from 2D inputs is a fundamental task in computer vision and graphics, serving as a cornerstone for understanding and interacting with the physical world. While traditional methods achieve high fidelity, they are limited by slow per-scene optimization or category-specific training, which hinders their practical deployment and scalability. Hence, generalizable feed-forward 3D reconstruction has witnessed rapid development in recent years. By learning a model that maps images directly to 3D representations in a single forward pass, these methods enable efficient reconstruction and robust cross-scene generalization. Our survey is motivated by a critical observation: despite the diverse geometric output representations, ranging from implicit fields to explicit primitives, existing feed-forward approaches share similar high-level architectural patterns, such as image feature extraction backbones, multi-view information fusion mechanisms, and geometry-aware design principles. Consequently, we abstract away from these representation differences and instead focus on model design, proposing a novel taxonomy centered on model design strategies that are agnostic to the output format. Our proposed taxonomy organizes the research directions into five key problems that drive recent research development: feature enhancement, geometry awareness, model efficiency, augmentation strategies and temporal-aware models. To support this taxonomy with empirical grounding and standardized evaluation, we further comprehensively review related benchmarks and datasets, and extensively discuss and categorize real-world applications based on feed-forward 3D models. Finally, we outline future directions to address open challenges such as scalability, evaluation standards, and world modeling.

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.

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.

3D Gaussian Splatting (3DGS) has emerged as a prominent paradigm for 3D reconstruction and novel view synthesis. However, it remains vulnerable to severe artifacts when trained under sparse-view constraints. While recent methods attempt to rectify artifacts in rendered views using image diffusion models, they typically rely on multi-view self-attention to retrieve information from reference images. We observe that this mechanism often fails when the rendered novel views output by 3DGS are heavily corrupted: damaged query features lead to erroneous cross-view retrieval, resulting in inconsistent rendering refinement. To address this, we propose GeoQuery, a geometry-guided diffusion framework that integrates generative priors with explicit geometric cues via a novel Geometry-guided Cross-view Attention (GCA) mechanism. First, by leveraging predicted depth maps and camera poses, we construct a geometry-induced correspondence field to sample reference features, forming a geometry-aligned proxy query that replaces the corrupted rendering features. Furthermore, we design a new cross-view feature aggregation pipeline, in which we restrict the cross-view attention to a local window around each proxy query to effectively retrieve useful features while suppressing spurious matches. GeoQuery can be seamlessly integrated into existing diffusion-based pipelines, enabling robust reconstruction even under extreme view sparsity. Extensive experiments on sparse-view novel view synthesis and rendering artifact removal demonstrate the effectiveness of our approach.

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks and numerical methods. We show how our GNPs can be trained to learn robust latent representations for the differential geometry of point-clouds to provide estimates of metric, curvature, and other shape-related features. We demonstrate how our pre-trained GNPs can be used (i) to estimate the geometric properties of surfaces of arbitrary shape and topologies with robustness in the presence of noise, (ii) to approximate solutions of geometric partial differential equations (PDEs) on manifolds, and (iii) to solve equations for shape deformations such as curvature driven flows. We release codes and weights for using GNPs in the package geo_neural_op. This allows for incorporating our pre-trained GNPs as components for reuse within existing and new data processing pipelines. The GNPs also can be used as part of numerical solvers involving geometry or as part of methods for performing inference and other geometric tasks.

3D object generation has undergone significant advancements, yielding high-quality results. However, fall short of achieving precise user control, often yielding results that do not align with user expectations, thus limiting their applicability. User-envisioning 3D object generation faces significant challenges in realizing its concepts using current generative models due to limited interaction capabilities. Existing methods mainly offer two approaches: (i) interpreting textual instructions with constrained controllability, or (ii) reconstructing 3D objects from 2D images. Both of them limit customization to the confines of the 2D reference and potentially introduce undesirable artifacts during the 3D lifting process, restricting the scope for direct and versatile 3D modifications. In this work, we introduce Interactive3D, an innovative framework for interactive 3D generation that grants users precise control over the generative process through extensive 3D interaction capabilities. Interactive3D is constructed in two cascading stages, utilizing distinct 3D representations. The first stage employs Gaussian Splatting for direct user interaction, allowing modifications and guidance of the generative direction at any intermediate step through (i) Adding and Removing components, (ii) Deformable and Rigid Dragging, (iii) Geometric Transformations, and (iv) Semantic Editing. Subsequently, the Gaussian splats are transformed into InstantNGP. We introduce a novel (v) Interactive Hash Refinement module to further add details and extract the geometry in the second stage. Our experiments demonstrate that Interactive3D markedly improves the controllability and quality of 3D generation. Our project webpage is available at https://interactive-3d.github.io/.

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.

Learning a 4D scene representation from a single monocular video that supports dynamic novel-view synthesis while maintaining faithful geometry over time remains challenging. Dynamic Gaussian Splatting achieves strong rendering performance through photometric optimization, yet does not explicitly enforce multi-view geometric consistency. In contrast, 3D foundation models recover coherent scene geometry and camera motion, but their point-based outputs are not designed for photorealistic rendering. We propose Ground4D, a geometry-grounded framework built on two stages. First, we perform geometry initialization via 3D foundation models, leveraging VGGT in a training-free manner to reconstruct multi-view-consistent 3D geometry and camera poses from monocular video. The recovered geometry provides a structured and reliable initialization for dynamic Gaussian representations. Second, we conduct geometry-consistency-aware refinement via dynamic Gaussian Splatting, optimizing the representation through differentiable rendering while maintaining multi-view geometric consistency across both observed and synthesized viewpoints. Furthermore, Ground4D inherently models the continuous 4D dynamics of the scene, naturally supporting rendering at arbitrary timestamps. By integrating foundation-level geometric priors into dynamic Gaussian optimization, Ground4D achieves stronger reconstruction fidelity and rendering performance, underscoring the role of geometry-grounded constraints in robust 4D scene modeling.

With the growing demand for high-fidelity 3D models from 2D images, existing methods still face significant challenges in accurately reproducing fine-grained geometric details due to limitations in domain gaps and inherent ambiguities in RGB images. To address these issues, we propose Hi3DGen, a novel framework for generating high-fidelity 3D geometry from images via normal bridging. Hi3DGen consists of three key components: (1) an image-to-normal estimator that decouples the low-high frequency image pattern with noise injection and dual-stream training to achieve generalizable, stable, and sharp estimation; (2) a normal-to-geometry learning approach that uses normal-regularized latent diffusion learning to enhance 3D geometry generation fidelity; and (3) a 3D data synthesis pipeline that constructs a high-quality dataset to support training. Extensive experiments demonstrate the effectiveness and superiority of our framework in generating rich geometric details, outperforming state-of-the-art methods in terms of fidelity. Our work provides a new direction for high-fidelity 3D geometry generation from images by leveraging normal maps as an intermediate representation.

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.

Multimodal large language models (MLLMs) have exhibited remarkable performance in various visual tasks, yet still struggle with spatial reasoning. Recent efforts mitigate this by injecting geometric features from 3D foundation models, but rely on static single-layer extractions. We identify that such an approach induces a task misalignment bias: the geometric features naturally evolve towards 3D pretraining objectives, which may contradict the heterogeneous spatial demands of MLLMs, rendering any single layer fundamentally insufficient. To resolve this, we propose GeoAlign, a novel framework that dynamically aggregates multi-layer geometric features to realign with the actual demands. GeoAlign constructs a hierarchical geometric feature bank and leverages the MLLM's original visual tokens as content-aware queries to perform layer-wise sparse routing, adaptively fetching the suitable geometric features for each patch. Extensive experiments on VSI-Bench, ScanQA, and SQA3D demonstrate that our compact 4B model effectively achieves state-of-the-art performance, even outperforming larger existing MLLMs.

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}.

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.

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.

Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints. We study open-ended geometric synthesis from natural language: translating free-form descriptions into precise constructions whose entities must simultaneously satisfy dozens of interacting constraints. To make this tractable, we release PyGeoX, a programmable geometric DSL that compiles declarative constraints into a differentiable loss, and PyGeoX-Bench, a stratified suite of 300 problems with per-constraint verifiable rewards. Using PyGeoX as a verifier, we identify a failure mode we call Outlier Gradient Masking: under global-norm rewards (any scheme that aggregates residuals through a single norm, for example, exp(-MSE)), a single outlier constraint can nullify the learning signal across all others. To address this, we propose Saturating Additive Rewards (SAR), which decompose the reward into bounded per-constraint terms, preserving partial progress and ensuring consistent gradients even under severe violations. Against MSE-based rewards, the natural baseline for geometry solvers, SAR improves the hard-tier solving rate by 2.3times, and the resulting 8B model is competitive with much larger frontier systems on this benchmark. We release the engine, benchmark, and data at https://github.com/Huawei-AI4Math/PyGeoX.

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.

3D vector graphics play a crucial role in various applications including 3D shape retrieval, conceptual design, and virtual reality interactions due to their ability to capture essential structural information with minimal representation. While recent approaches have shown promise in generating 3D vector graphics, they often suffer from lengthy processing times and struggle to maintain view consistency. To address these limitations, we propose ViewCraft3D (VC3D), an efficient method that leverages 3D priors to generate 3D vector graphics. Specifically, our approach begins with 3D object analysis, employs a geometric extraction algorithm to fit 3D vector graphics to the underlying structure, and applies view-consistent refinement process to enhance visual quality. Our comprehensive experiments demonstrate that VC3D outperforms previous methods in both qualitative and quantitative evaluations, while significantly reducing computational overhead. The resulting 3D sketches maintain view consistency and effectively capture the essential characteristics of the original objects.

We propose CAD-Assistant, a general-purpose CAD agent for AI-assisted design. Our approach is based on a powerful Vision and Large Language Model (VLLM) as a planner and a tool-augmentation paradigm using CAD-specific modules. CAD-Assistant addresses multimodal user queries by generating actions that are iteratively executed on a Python interpreter equipped with the FreeCAD software, accessed via its Python API. Our framework is able to assess the impact of generated CAD commands on geometry and adapts subsequent actions based on the evolving state of the CAD design. We consider a wide range of CAD-specific tools including Python libraries, modules of the FreeCAD Python API, helpful routines, rendering functions and other specialized modules. We evaluate our method on multiple CAD benchmarks and qualitatively demonstrate the potential of tool-augmented VLLMs as generic CAD task solvers across diverse CAD workflows.

Automatic 3D content creation has achieved rapid progress recently due to the availability of pre-trained, large language models and image diffusion models, forming the emerging topic of text-to-3D content creation. Existing text-to-3D methods commonly use implicit scene representations, which couple the geometry and appearance via volume rendering and are suboptimal in terms of recovering finer geometries and achieving photorealistic rendering; consequently, they are less effective for generating high-quality 3D assets. In this work, we propose a new method of Fantasia3D for high-quality text-to-3D content creation. Key to Fantasia3D is the disentangled modeling and learning of geometry and appearance. For geometry learning, we rely on a hybrid scene representation, and propose to encode surface normal extracted from the representation as the input of the image diffusion model. For appearance modeling, we introduce the spatially varying bidirectional reflectance distribution function (BRDF) into the text-to-3D task, and learn the surface material for photorealistic rendering of the generated surface. Our disentangled framework is more compatible with popular graphics engines, supporting relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments that show the advantages of our method over existing ones under different text-to-3D task settings. Project page and source codes: https://fantasia3d.github.io/.

In this paper, we present a deep learning-based framework for solving geometric construction problems through visual reasoning, which is useful for automated geometry theorem proving. Constructible problems in geometry often ask for the sequence of straightedge-and-compass constructions to construct a given goal given some initial setup. Our EuclidNet framework leverages the neural network architecture Mask R-CNN to extract the visual features from the initial setup and goal configuration with extra points of intersection, and then generate possible construction steps as intermediary data models that are used as feedback in the training process for further refinement of the construction step sequence. This process is repeated recursively until either a solution is found, in which case we backtrack the path for a step-by-step construction guide, or the problem is identified as unsolvable. Our EuclidNet framework is validated on complex Japanese Sangaku geometry problems, demonstrating its capacity to leverage backtracking for deep visual reasoning of challenging problems.

Vision-language models solve geometry problems with rising accuracy, yet their intermediate states remain latent and unverifiable: a relation expressed in textual reasoning or drawing code carries no guarantee that a constraint-satisfying configuration realizes it. We observe that existing externalization methods based on rendered pixels or one-shot scripts fail to provide exact, per-action geometric guarantees. Enforcing geometric relations by algebraic definition closes this gap: the workspace becomes a constraint-checked evolving canvas. We present Draw2Think, a framework that recasts geometric reasoning from latent spatial inference into agentic interaction with the GeoGebra constraint engine. In a Propose-Draw-Verify loop, Draw2Think externalizes hypotheses onto an executable canvas, measures exact geometric quantities, and feeds structured observations back to the model, so subsequent reasoning proceeds from checked canvas state grounded by the shared workspace. This externalization makes two properties separately auditable: model-level Construction Fidelity (whether the canvas realizes the intended configuration) and engine-level Measurement Faithfulness (exact values and relations from canvas constraints). Across construction, outcome, and rendering evaluations, Draw2Think builds canvases that pass 95.9% predicate-level and 84.0% strict problem-level construction checks on GeoGoal, improves outcome accuracy by up to 4.1%/16.4% on planar/solid benchmarks, and attains 68.2%/90.5% strict/relaxed rendering scores on GenExam-math. Project page is available at https://draw2think.github.io/

Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since most geometric proofs rely on intuitive diagrams, verifying geometry problems is particularly challenging. To address these gaps, we introduce LeanGeo, a unified formal system for formalizing and solving competition-level geometry problems within the Lean 4 theorem prover. LeanGeo features a comprehensive library of high-level geometric theorems with Lean's foundational logic, enabling rigorous proof verification and seamless integration with Mathlib. We also present LeanGeo-Bench, a formal geometry benchmark in LeanGeo, comprising problems from the International Mathematical Olympiad (IMO) and other advanced sources. Our evaluation demonstrates the capabilities and limitations of state-of-the-art Large Language Models on this benchmark, highlighting the need for further advancements in automated geometric reasoning. We open source the theorem library and the benchmark of LeanGeo at https://github.com/project-numina/LeanGeo/tree/master.