Daily Papers

Reconstructing articulated objects from sparse images requires recovering complete geometry, movable parts, and motion parameters. Recent methods typically separate geometry reconstruction, part reasoning, and articulation estimation into different stages. This separation can weaken consistency between shape, active parts, and motion, while also incurring substantial inference cost. We introduce Artic-O, an end-to-end, feed-forward framework for articulated object reconstruction via latent geometry learning. Instead of fitting geometry in image or view space, Artic-O maps sparse multi-state observations into a pretrained latent geometry space, where a frozen flow-matching decoder provides a complete-shape prior for recovering visible and occluded structures. To connect geometry with articulation, Artic-O fuses visual tokens, geometry latents, and point-wise decoder features in an image-grounded part-reasoning module for active-part segmentation and articulation prediction. We further train the model with a geometry-to-articulation curriculum and a decoupled two-pass strategy to balance reconstruction and part-level supervision. On PartNet-Mobility, Artic-O achieves strong reconstruction quality while being substantially more efficient than LARM, a strong prior method. It reduces Chamfer Distance, improves F-score, and achieves comparable or better articulation accuracy across most joint metrics, while reducing inference time from 9 minutes to about 0.3 seconds per object.

RNA function arises from the coupling of nucleotide sequence and three-dimensional structure, motivating their joint design. Coordinating global folding with nucleotide-level detail remains challenging under limited structural supervision. We introduce La-Ribo, a generative framework for RNA sequence-structure co-design via geometry-latent flow matching. La-Ribo retains a sparse phosphate-sugar--base scaffold and encodes nucleotide identity and local conformation in residue-wise latents. A shared flow network generates both jointly, and an RNA-specific decoder then reconstructs all heavy atoms. To expand supervision, we construct a quality-controlled corpus of 168,561 RNA structures, integrating experimental data with predictions from three folding models, including 10,631 MSA-supported structures generated in this work. La-Ribo improves designability and codesignability over the evaluated baselines across sampling budgets and two refolding models, and the same prior supports scaffold-conditioned inverse folding without additional training.

We present VGGT-Diff, a geometry-routed multi-view diffusion model for sparse-view novel view synthesis. Existing novel view synthesis (NVS) methods face a fundamental trade-off: reconstruction-based approaches preserve observed geometry but struggle to synthesize unseen regions, while diffusion-based methods provide strong generative priors yet rely on implicit source-to-query correspondence. VGGT-Diff bridges these regimes by routing visual geometry latents from VGGT-Ω into a pretrained video diffusion model. Each visual token is associated with a 3D point and confidence, then transformed into query-aligned latent conditions through a confidence-aware Visual Geometry Router (VGR) that preserves front and back surface evidence. These conditions guide joint target-view denoising, while Point-Track Residual Consistency (PTRC) regularizes predicted-clean residuals along reliable 3D tracks, improving multi-view stability. We further introduce robust geometry conditioning, combining training-time regularization with inference-time guidance for improved robustness. Experiments show competitive or state-of-the-art performance across interpolation and extrapolation under different viewpoint difficulties. Our code is available at https://github.com/chenkangjie1123/VGGT-Diff.

We present NaTex, a native texture generation framework that predicts texture color directly in 3D space. In contrast to previous approaches that rely on baking 2D multi-view images synthesized by geometry-conditioned Multi-View Diffusion models (MVDs), NaTex avoids several inherent limitations of the MVD pipeline. These include difficulties in handling occluded regions that require inpainting, achieving precise mesh-texture alignment along boundaries, and maintaining cross-view consistency and coherence in both content and color intensity. NaTex features a novel paradigm that addresses the aforementioned issues by viewing texture as a dense color point cloud. Driven by this idea, we propose latent color diffusion, which comprises a geometry-awared color point cloud VAE and a multi-control diffusion transformer (DiT), entirely trained from scratch using 3D data, for texture reconstruction and generation. To enable precise alignment, we introduce native geometry control that conditions the DiT on direct 3D spatial information via positional embeddings and geometry latents. We co-design the VAE-DiT architecture, where the geometry latents are extracted via a dedicated geometry branch tightly coupled with the color VAE, providing fine-grained surface guidance that maintains strong correspondence with the texture. With these designs, NaTex demonstrates strong performance, significantly outperforming previous methods in texture coherence and alignment. Moreover, NaTex also exhibits strong generalization capabilities, either training-free or with simple tuning, for various downstream applications, e.g., material generation, texture refinement, and part segmentation and texturing.

3D part decomposition is a central capability for editable asset creation, yet existing workflows typically segment a completed mesh as a post-processing step, making the result sensitive to geometric artifacts, texture ambiguity, and limited part-level annotations. We present OmniLatent, a unified latent modeling framework for 3D part decomposition. Instead of predicting part labels in isolation, OmniLatent learns a shared latent space that jointly encodes geometry, deformation, appearance, and binary part IDs, allowing data-rich geometric and visual priors to support data-scarce part learning. Given a single input image, the base model generates geometry, deformation, texture, and surface part IDs in one pass, producing a part-aware 3D asset without a separate segmentation stage. We further tune the pretrained model for two extensions: a point-prompt adapter that maps arbitrary 3D point prompts with binary part IDs into latent tokens for full segmentation, refinement, and part subdivision, and an amodal part completion model that completes partial surface masks into a coherent full-object decomposition through dynamic per-part token allocation, cross-attention to the given geometry latent, and alternating part-local and global attention. Extensive experiments show that OmniLatent produces semantically meaningful part segmentations with precise boundaries, supports interactive part editing, and completes partial part observations while preserving global object consistency.

Current feed-forward 3D/4D reconstruction systems rely on dense geometry and pose supervision -- expensive to obtain at scale and particularly scarce for dynamic real-world scenes. We present Flow3r, a framework that augments visual geometry learning with dense 2D correspondences (`flow') as supervision, enabling scalable training from unlabeled monocular videos. Our key insight is that the flow prediction module should be factored: predicting flow between two images using geometry latents from one and pose latents from the other. This factorization directly guides the learning of both scene geometry and camera motion, and naturally extends to dynamic scenes. In controlled experiments, we show that factored flow prediction outperforms alternative designs and that performance scales consistently with unlabeled data. Integrating factored flow into existing visual geometry architectures and training with {sim}800K unlabeled videos, Flow3r achieves state-of-the-art results across eight benchmarks spanning static and dynamic scenes, with its largest gains on in-the-wild dynamic videos where labeled data is most scarce.

Existing 3D scene editing methods typically rely on per-scene optimization over explicit 3D representations or cascaded edit-and-reconstruct pipelines, resulting in high test-time cost, limited 3D awareness, and structural inconsistencies. To couple appearance synthesis and geometry prediction during editing, we build on a unified RGB-geometry reconstruction-generation latent space and adapt it to feed-forward 3D scene editing. The resulting framework, JointEdit3D, performs asymmetric latent inpainting by observing only a single edited RGB reference latent and generating the remaining RGB views and edited geometry latent under source-scene anchoring. JointEdit3D introduces a dedicated SceneAnchor Branch to inject source-scene structure without forcing direct copying, and adopts edit/background-aware losses to balance edited-region fidelity with unedited-content preservation. To address the lack of paired resources for standardized 3D scene editing evaluation, we introduce SceneEdit3D-15K, a dataset with 15K paired editing samples and renderer-provided 3D annotations, together with SceneEdit3D-Bench, a curated 100-sample benchmark. Experiments show that JointEdit3D improves edited-region quality and 3D structural completeness over prior baselines while maintaining competitive background preservation.

Dense 3D tracking from monocular video is fundamental to dynamic scene understanding. While recent 3D foundation models provide reliable per-frame geometry, recovering object motion in this geometry remains challenging and benefits from strong motion priors learned from real-world videos. Existing 3D trackers either follow iterative paradigms trained from scratch on synthetic data or fine-tune 3D reconstruction models learned from static multi-view images, both lacking real-world motion priors. Pre-trained video diffusion transformers (video DiTs) offer rich spatio-temporal priors from internet-scale videos, making them a promising foundation for 3D tracking. However, their frame-anchored formulation, which generates each frame's content, is fundamentally mismatched with reference-anchored dense 3D tracking, which must follow the same physical points from a reference frame across time. We present TrackCraft3R, the first method to repurpose a video DiT as a feed-forward dense 3D tracker. Given a monocular video and its frame-anchored reconstruction pointmap, TrackCraft3R predicts a reference-anchored tracking pointmap that follows every pixel of the first frame across time in a single forward pass, along with its visibility. We achieve this through two designs: (i) a dual-latent representation that uses per-frame geometry latents and reference-anchored track latents as dense queries, and (ii) temporal RoPE alignment, which specifies the target timestamp of each track latent. Together, these designs convert the per-frame generative paradigm of video DiTs into a reference-anchored tracking formulation with LoRA fine-tuning. TrackCraft3R achieves state-of-the-art performance on standard sparse and dense 3D tracking benchmarks, while running 1.3x faster and using 4.6x less peak memory than the strongest prior method. We further demonstrate robustness to large motions and long videos.

Learning large-scale vision-language-action (VLA) models from multi-embodiment datasets remains challenging due to heterogeneous action spaces across end effectors. Although latent action models (LAMs) can learn embodiment-agnostic action representations from diverse video data, existing image-based LAMs often fail to capture fine-grained end-effector articulation, particularly finger-level geometric changes in human and dexterous robot hands. To address this limitation, we propose GALA, a Geometry-Aware Latent-Action modeling framework that augments image-based latent actions with 3D end-effector geometric motion. However, naively incorporating point clouds yields fine-grained action representations with limited shared semantics, hindering cross-embodiment pretraining. To address this issue, we introduce the Unified End-effector Motion Representation (UEMR), which preserves fine-grained motion information while improving the cross-embodiment generalizability of latent actions. Building upon UEMR, GALA combines visual latent actions that capture scene-level dynamics with geometric latent actions that capture shared fine-grained end-effector articulation, providing effective supervision for VLA pretraining from multi-embodiment data, including action-free ego-centric human videos. Experiments on fine-grained motion probing, cross-embodiment retrieval, and downstream VLA evaluation demonstrate GALA's effectiveness in modeling generalizable fine-grained motions across embodiments, achieving 68.3% RoboCasa-GR1 success rate and 75.5% real-world success rate. Code, appendix, and demos are available at https://puzhenyuan.github.io/GALA-website/.

Despite progress in vision-language models, 3D spatial reasoning from 2D images remains challenging. Text-based methods describe intermediate geometry with discrete tokens, limiting fidelity for continuous spatial relations. Continuous latents offer richer representations, but a single latent type does not explicitly separate the cues needed across spatial tasks. Decomposed spatial latents address this by representing position, direction, and global geometry separately under geometric supervision. Yet the geometry representation can still collapse toward one dominant direction, and unrestricted attention can leave the latents underused during answer learning. We introduce GeoLatent, combining Common--Residual Geometry Alignment (CR-GEO) with routed optimization to structure the geometry states while promoting latent-mediated answer learning. CR-GEO separates shared from residual teacher geometry; routed optimization jointly trains geometry and language, temporarily directs visual answer learning through the latents, and restores full attention with geometry supervision. In controlled comparisons, CR-GEO raises geometry effective rank from 1.00 to 3.87, while blocking latent readout at the bottleneck lowers direction accuracy from 89.1% to 25.8% on 128 fixed questions. After recovery, the differentiated geometry representation and latent-mediated visual route remain available alongside direct image access. GeoLatent achieves 73.0% on SPAR-Bench and 72.1% on SPBench, outperforming previously reported methods on both.

Recent work has shown that neural networks can perform 3D tasks such as Novel View Synthesis (NVS) without explicit 3D reconstruction. Even so, we argue that strong 3D inductive biases are still helpful in the design of such networks. We show this point by introducing LagerNVS, an encoder-decoder neural network for NVS that builds on `3D-aware' latent features. The encoder is initialized from a 3D reconstruction network pre-trained using explicit 3D supervision. This is paired with a lightweight decoder, and trained end-to-end with photometric losses. LagerNVS achieves state-of-the-art deterministic feed-forward Novel View Synthesis (including 31.4 PSNR on Re10k), with and without known cameras, renders in real time, generalizes to in-the-wild data, and can be paired with a diffusion decoder for generative extrapolation.

Latent flow matching for image generation usually transports Gaussian noise to variational autoencoder latents along linear paths. Both endpoints, however, concentrate in thin spherical shells, and a Euclidean chord leaves those shells even when preprocessing aligns their radii. By decomposing each latent token into radial and angular components, we show through component-swap probes that decoded perceptual and semantic content is carried predominantly by direction, with radius contributing much less. We therefore project data latents onto a fixed token radius, use the radial projection of Gaussian noise as the spherical prior, finetune the decoder with the encoder frozen, and replace linear interpolation with spherical linear interpolation. The resulting geodesic paths stay on the sphere at every timestep, and their velocity targets are purely angular by construction. Under matched training, the method consistently improves class-conditional ImageNet-256 FID across different image tokenizers, leaves the diffusion architecture unchanged, and requires no auxiliary encoder or representation-alignment objective.

We present a compact geometry-native latent space as a shared foundation for perception and generation. Visual generators can produce photorealistic frames without preserving a consistent 3D scene. We argue that this is not only a modeling problem but also a representation problem: generators typically evolve appearance-centric latents, while perception models recover geometry in a semantically rich space that encodes cross-view structure. Rather than adding geometry as another output, we reparameterize a geometry foundation model's features into a compact latent space for generation. We realize this shift with the geometry-native autoencoder (GAE), whose latent is jointly decodable to appearance, depth, cameras, and point maps. With this state, a standard conditional flow supports diverse generation tasks. In controlled comparisons that hold the generator and training protocol fixed, replacing the latent with GAE improves both visual quality and independently measured 3D coherence: FVD falls by 12.7% and 23.1% on RealEstate10K and DL3DV, and camera-trajectory error is halved on RealEstate10K. Together, these results show that the latent space is central to geometry-consistent generation and can serve as a shared interface between perception and generation.

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}.

Neural networks can accurately forecast complex dynamical systems, yet how they internally represent underlying latent geometry remains poorly understood. We study neural forecasters through the lens of representational alignment, introducing anchor-based, geometry-agnostic relative embeddings that remove rotational and scaling ambiguities in latent spaces. Applying this framework across seven canonical dynamical systems - ranging from periodic to chaotic - we reveal reproducible family-level structure: multilayer perceptrons align with other MLPs, recurrent networks with RNNs, while transformers and echo-state networks achieve strong forecasts despite weaker alignment. Alignment generally correlates with forecasting accuracy, yet high accuracy can coexist with low alignment. Relative geometry thus provides a simple, reproducible foundation for comparing how model families internalize and represent dynamical structure.

We identify the Spectral Energy Gain in extreme model compression, where low-rank binary approximations outperform tiny-rank floating-point baselines for heavy-tailed spectra. However, prior attempts fail to realize this potential, trailing state-of-the-art 1-bit methods. We attribute this degradation to Latent Geometry Misalignment: standard singular vectors exhibit high coherence (spiky distribution), the worst-case geometry for binary quantization. To realize this gain, we propose LittleBit-2, a framework employing Internal Latent Rotation and Joint Iterative Quantization (Joint-ITQ). This approach acts as a geometric preconditioner, aligning coherent latent distributions with the binary hypercube with zero inference overhead. Empirically, LittleBit-2 establishes a new state-of-the-art in the sub-1-bit regime (1sim0.1 bpp) on Llama-2 and Llama-3, matching the fidelity of leading 1-bit baselines.

We investigate whether independently trained language models converge to geometrically compatible latent representations, and whether this compatibility can be exploited to correct model behavior at inference time without any weight updates. We learn a linear projection matrix that maps activation vectors from a large teacher model into the coordinate system of a smaller student model, then intervene on the student's residual stream during generation by substituting its internal state with the translated teacher representation. Across a fully crossed experimental matrix of 20 heterogeneous teacher-student pairings spanning mixture-of-experts, dense, code-specialized, and synthetically trained architectures, the Ridge projection consistently achieves R^2 = 0.50 on verbal reasoning and R^2 = 0.40 on mathematical reasoning, collapsing to R^2 = -0.22 under permutation control and R^2 = 0.01 under L_1 regularization. Behavioral correction rates range from 14.0% to 50.0% on TruthfulQA (mean 25.2%) and from 8.5% to 43.3% on GSM8K arithmetic reasoning (mean 25.5%), demonstrating that the method generalizes across fundamentally different reasoning domains. We report a near-zero correlation between geometric alignment quality and behavioral correction rate (r = -0.07), revealing a dissociation between representation space fidelity and output space impact. Intervention strength is architecture-specific: student models exhibit characteristic sensitivity profiles that invert across domains, with the most steerable verbal student becoming the least steerable mathematical student. Finally, a double dissociation experiment conducted across all 20 model pairings confirms without exception that projection matrices collapse catastrophically when transferred across reasoning domains (mean R^2 = -3.83 in both transfer directions), establishing domain-specific subspace geometry as a universal property of LMs.

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.

Alignment is no longer a luxury, it is a necessity. As large language models (LLMs) enter high-stakes domains like education, healthcare, governance, and law, their behavior must reliably reflect human-aligned values and safety constraints. Yet current evaluations rely heavily on behavioral proxies such as refusal rates, G-Eval scores, and toxicity classifiers, all of which have critical blind spots. Aligned models are often vulnerable to jailbreaking, stochasticity of generation, and alignment faking. To address this issue, we introduce the Alignment Quality Index (AQI). This novel geometric and prompt-invariant metric empirically assesses LLM alignment by analyzing the separation of safe and unsafe activations in latent space. By combining measures such as the Davies-Bouldin Score (DBS), Dunn Index (DI), Xie-Beni Index (XBI), and Calinski-Harabasz Index (CHI) across various formulations, AQI captures clustering quality to detect hidden misalignments and jailbreak risks, even when outputs appear compliant. AQI also serves as an early warning signal for alignment faking, offering a robust, decoding invariant tool for behavior agnostic safety auditing. Additionally, we propose the LITMUS dataset to facilitate robust evaluation under these challenging conditions. Empirical tests on LITMUS across different models trained under DPO, GRPO, and RLHF conditions demonstrate AQI's correlation with external judges and ability to reveal vulnerabilities missed by refusal metrics. We make our implementation publicly available to foster future research in this area.

Camera-based autonomous driving perception requires a shared representation that preserves metric 3D structure across synchronized multi-camera streams. However, existing image-based frameworks often rely on backbones pretrained for semantic recognition, and introduce 3D geometry through downstream task-specific modules. As a result, their shared representations may fail to preserve explicit metric geometry and consistent 3D scene structure. In this paper, we present a Geometry-grounded Unified 3D Perception (GeoUP) framework that adapts the reconstruction-oriented latent of VGGT to calibrated, streaming multi-camera driving scenes. GeoUP factorizes cross-image interaction into self, temporal, and view attention to capture structurally distinct temporal and cross-view correspondences. It further injects calibration-aware raymap encodings to provide metric scale and camera geometry. The resulting geometry-grounded latent is decoded for metric depth estimation, 3D object detection, and semantic occupancy prediction, corresponding to surface-, instance-, and volume-level readouts of the same 3D scene. Through joint multi-task and multi-dataset training, GeoUP effectively leverages heterogeneous annotations and generalizes across diverse sensor configurations and perception ranges. Extensive experiments on nuScenes, Argoverse 2, Waymo, KITTI, and DDAD demonstrate that GeoUP achieves SOTA performance across detection, occupancy, and depth estimation. These results validate the effectiveness of geometry-grounded representations for unified 3D driving perception.

As large language models (LLMs) are increasingly deployed in alignment-sensitive contexts, activation steering has emerged as a lightweight, inference-time alternative to fine-tuning methods (e.g., RLHF, DPO) for behavioral control. However, existing work typically validates steering on isolated behaviors, leaving it unclear whether steering vectors encode coherent semantic structure or merely exploit behavior-specific shortcuts. We investigate whether the latent geometry of LLM steering vectors reflects theory-specified structure in human values and morality. Using Schwartz's Theory of Basic Human Values as our primary fine-grained framework, we introduce a 26K-sample benchmark covering 20 human values and analyze distribution-driven methods (e.g., CAA, SphericalSteer, ODESteer) and behavior-centric approaches (e.g., COLD-Steer, BiPO) across diverse model families and sizes. We find that distribution-driven methods recover human value topologies aligned with theoretical predictions (Spearman ρ up to 0.51, p < 10^{-13}). In contrast, behavior-centric methods achieve comparable steering performance but show little correlation with the expected value geometry. Geometric fidelity improves with model scale but drops after instruction tuning. Finally, better geometric alignment also leads to more human-consistent transfer across values: steering one value correctly lifts compatible values and suppresses opposing ones. Code and data are available at: https://github.com/DeepRCL/Steering_Geometry.

Prediction errors from video world models are often treated as physical surprise, but they can also reflect appearance, static content, motion, or ordinary prediction difficulty. We present an evaluation framework that separates what frozen representations contain, how they organize appearance and physical differences, and what changes a model's own prediction error. On IntPhys2, a benchmark of physically possible and impossible events, we compare representations from latent prediction, masked pixel reconstruction, and simple visual statistics. Appearance remains easy to decode, while V-JEPA2 exposes modest information about whether events are possible or impossible. Looking at the latent geometry, appearance changes become smaller compared with differences between videos, their directions line up more consistently across scenes, and their overlap with physical changes decreases in deeper layers. Across action-conditioned models, incorrect actions raise prediction error, while appearance changes also produce substantial responses. In Physion++ video clips, repeating a single frame can produce higher error than the original clip, while changing color throughout the clip can lower it. Using Kubric, a simulation and rendering framework, we find that impossible events can produce lower error than possible events. A fixed error threshold also incorrectly flags many possible events as impossible. A model can therefore represent physical information and respond to incorrect actions without its native prediction error reliably measuring physical surprise.

Large-scale video diffusion models achieve impressive visual quality, yet often fail to preserve geometric consistency. Prior approaches improve consistency either by augmenting the generator with additional modules or applying geometry-aware alignment. However, architectural modifications can compromise the generalization of internet-scale pretrained models, while existing alignment methods are limited to static scenes and rely on RGB-space rewards that require repeated VAE decoding, incurring substantial compute overhead and failing to generalize to highly dynamic real-world scenes. To preserve the pretrained capacity while improving geometric consistency, we propose VGGRPO (Visual Geometry GRPO), a latent geometry-guided framework for geometry-aware video post-training. VGGRPO introduces a Latent Geometry Model (LGM) that stitches video diffusion latents to geometry foundation models, enabling direct decoding of scene geometry from the latent space. By constructing LGM from a geometry model with 4D reconstruction capability, VGGRPO naturally extends to dynamic scenes, overcoming the static-scene limitations of prior methods. Building on this, we perform latent-space Group Relative Policy Optimization with two complementary rewards: a camera motion smoothness reward that penalizes jittery trajectories, and a geometry reprojection consistency reward that enforces cross-view geometric coherence. Experiments on both static and dynamic benchmarks show that VGGRPO improves camera stability, geometry consistency, and overall quality while eliminating costly VAE decoding, making latent-space geometry-guided reinforcement an efficient and flexible approach to world-consistent video generation.

JEPA-style latent world models can use Euclidean distance to a goal latent as the cost for model-predictive control (MPC). Strong decoding of task variables, however, does not guarantee that this particular cost ranks candidate action sequences by real task progress. We call the latter property decision-metric alignment. We introduce Plan-Real Spearman, which measures latent--real rank agreement on random plans, and CEM-stage Spearman, which measures the same agreement as cross-entropy-method (CEM) search concentrates its proposal. We analyze sufficient conditions under which latent distance preserves real-cost rankings, identifying encoder distortion, terminal rollout error, and candidate margins as the controlling quantities. Guided by the observed empirical alignment gap, DA-LeWM augments LeWM with inverse-dynamics and demonstration-conditioned goal-action heads. Across all our experiments, DA-LeWM accelerates convergence and achieves higher online success than LeWM, while probe scores remain similar. These results show that action-conditioned objectives improve the geometry used by Euclidean-cost, CEM-based latent MPC.

Autonomous driving requires both safe and efficient planning decisions in dynamic 3D environments. Although recent Vision/Video-Action models learn policies directly from visual observations and scale well with advances in vision transformers and large-scale training data, they often lack explicit geometric grounding and future-aware spatial guidance, limiting their ability to balance collision avoidance and driving progress. In this work, we propose GeoWorldAD, a geometry world action model that grounds trajectory planning in ego-aligned 3D space and anticipates short-horizon scene evolution with latent future geometry tokens. Present geometry provides essential spatial constraints for safe planning, while future geometry reveals how surrounding agents and ego-centric free space may evolve, reducing overly conservative decisions without sacrificing safety. To efficiently exploit these geometric cues, GeoWorldAD progressively aggregates multi-scale present geometry and latent future geometry through iterative trajectory refinement. Experiments on NAVSIM v1 and v2 demonstrate state-of-the-art performance, highlighting the effectiveness of explicit 3D geometry grounding and future geometry world modeling for safe and efficient autonomous driving.

Physical trajectories contain more than snapshots of a system: they also reveal how its states evolve under governing conditions. However, representation learning for parametric partial differential equations (PDEs) has largely relied on reconstruction-based objectives that emphasize recovering observed physical fields. In this paper, we investigate predictive representation pretraining as an alternative to reconstruction-based learning. We find that predictive representations preserve rich physical information, yet this advantage alone does not ensure accurate field evolution. Based on these observations, we introduce PDE-JEPA for parametric PDE dynamics. Specifically, we first train an encoder using a masked-latent prediction to capture the underlying regularities of PDE dynamics. To explicitly adapt the pretrained representation toward a more dynamics-aligned state space, we then introduce a geometry projector that aligns latent trajectory geometry with the evolution geometry of physical fields. Finally, building on this geometry-aligned latent space, we further develop a physics-structured latent predictor that decomposes the dynamics into parameter-independent evolution and parameter-dependent response components. Extensive experiments on nine widely used PDE benchmarks demonstrate that our framework outperforms existing state-of-the-art methods by an average of 33.4\% in-distribution, while achieving an average improvement of 51.4\% when extrapolating to unseen governing parameters. The project page is available https://tanpig-x.github.io/PDE-JEPA/{here}.

Latent world models rely on representation geometry for planning, yet regularizing the latent marginal alone does not determine the state-to-state relationships used for action selection. We show that this can cause planning-relevant novelty structure to be weakened as representations are transformed into the final latent used by the planner. We introduce Aligned Transport of Latent Structure (ATLAS), a training objective that explicitly preserves relational geometry while calibrating the global latent distribution. ATLAS transfers normalized pairwise structure from an informative encoder representation to the planning latent and uses Wasserstein embedding matching (WEMReg) to calibrate its marginal through one-dimensional Wasserstein-2 transport. Our analysis shows that relational preservation and marginal calibration impose non-redundant constraints, and connects finite-candidate planning stability to relational distortion, latent-scale mismatch, and prediction error. Instantiated in LeWM, ATLAS improves mean goal-reaching success across PushT, TwoRoom, and OGBench-Cube on both lower- and higher-novelty evaluation subsets, with the largest gain on higher-novelty TwoRoom episodes. Representation and rollout diagnostics further show stronger novelty-related structure in the planning latent, improved marginal calibration, and lower multi-step prediction error. Together, these results highlight preservation of planning-relevant latent geometry as an important ingredient for reliable world-model planning. Code is available at https://anonymous.4open.science/r/atlas-world-model-72C4/.

Latent representations learned by neural networks often exhibit semantic structure, where concept similarity is reflected by geometric proximity in embedding space. However, comparing such spaces across models remains difficult: changes in architecture, pretraining data, objective, or random seed can yield embeddings with similar content but incompatible geometry. This latent space alignment problem is central to interpretability, transfer and multimodal learning, federated systems, and semantic communication; however, progress remains limited by the lack of large-scale, model-diverse, and metadata-rich benchmarks. To address this gap, we introduce SEMASIA, a large-scale collection of latent representations extracted from approximately 1,700 pretrained vision models across eight standard image-classification benchmarks. SEMASIA pairs embeddings with structured metadata describing architectures, training regimes, pretraining sources, and model scale. We demonstrate three applications of the resource. First, we analyze the conceptual organization of individual latent spaces, showing consistent prototype-like clustering and hierarchical semantic neighborhoods across models and datasets. Second, we benchmark supervised alignment mappings between latent spaces using reconstruction error and downstream task performance. Third, we perform a large-scale regression analysis of how pretraining-data complexity, specialization, transfer learning, augmentation, and model scale relate to geometric and probing properties of embeddings. By coupling representational scale with standardized metadata, SEMASIA provides a reproducible foundation for studying latent geometry, evaluating alignment methods, and developing next-generation heterogeneous and interoperable AI systems.

Cross-view geo-spatial learning consists of two important tasks: Cross-View Geo-Localization (CVGL) and Cross-View Image Synthesis (CVIS), both of which rely on establishing geometric correspondences between ground and aerial views. Recent Geometric Foundation Models (GFMs) have demonstrated strong capabilities in extracting generalizable 3D geometric features from images, but their potential in cross-view geo-spatial tasks remains underexplored. In this work, we present Geo^2, a unified framework that leverages Geometric priors from GFMs (e.g., VGGT) to jointly perform geo-spatial tasks, CVGL and bidirectional CVIS. Despite the 3D reconstruction ability of GFMs, directly applying them to CVGL and CVIS remains challenging due to the large viewpoint gap between ground and aerial imagery. We propose GeoMap, which embeds ground and aerial features into a shared 3D-aware latent space, effectively reducing cross-view discrepancies for localization. This shared latent space naturally bridges cross-view image synthesis in both directions. To exploit this, we propose GeoFlow, a flow-matching model conditioned on geometry-aware latent embeddings. We further introduce a consistency loss to enforce latent alignment between the two synthesis directions, ensuring bidirectional coherence. Extensive experiments on standard benchmarks, including CVUSA, CVACT, and VIGOR, demonstrate that Geo^2 achieves state-of-the-art performance in both localization and synthesis, highlighting the effectiveness of 3D geometric priors for cross-view geo-spatial learning.

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/

The boundary representation (B-Rep) is the standard data structure used in Computer-Aided Design (CAD) for defining solid models. Despite recent progress, directly generating B-Reps end-to-end with precise geometry and watertight topology remains a challenge. This paper presents AutoBrep, a novel Transformer model that autoregressively generates B-Reps with high quality and validity. AutoBrep employs a unified tokenization scheme that encodes both geometric and topological characteristics of a B-Rep model as a sequence of discrete tokens. Geometric primitives (i.e., surfaces and curves) are encoded as latent geometry tokens, and their structural relationships are defined as special topological reference tokens. Sequence order in AutoBrep naturally follows a breadth first traversal of the B-Rep face adjacency graph. At inference time, neighboring faces and edges along with their topological structure are progressively generated. Extensive experiments demonstrate the advantages of our unified representation when coupled with next-token prediction for B-Rep generation. AutoBrep outperforms baselines with better quality and watertightness. It is also highly scalable to complex solids with good fidelity and inference speed. We further show that autocompleting B-Reps is natively supported through our unified tokenization, enabling user-controllable CAD generation with minimal changes. Code is available at https://github.com/AutodeskAILab/AutoBrep.

State-of-the-art single-image 3D reconstruction methods often rely on complex hybrid architectures and loss functions, or compress geometry into latent spaces in order to leverage pre-trained latent diffusion models. In this work, we show that such architectural overhead and intricate loss formulations are unnecessary. We introduce a minimalist pixel-space Diffusion Transformer, built on a plain ViT, that operates directly on raw 3D point map patches and is conditioned on image tokens from a pre-trained DINOv3. Unlike existing latent diffusion approaches, we train our diffusion backbone entirely from scratch, eliminating the need for point map tokenizers. Despite its simplicity, our approach surpasses complex latent-based diffusion models while remaining significantly simpler than hybrid alternatives. Notably, it produces sharper geometric structure and is more robust in highly ambiguous regions, such as transparent objects.

Artificial neural networks (ANN) were inspired by the architecture and functions of the human brain and have revolutionised the field of artificial intelligence (AI). Inspired by studies on the latent geometry of the brain we posit that an increase in the research and application of hyperbolic geometry in machine learning will lead to increased accuracy, improved feature space representations and more efficient models across a range of tasks. We look at the structure and functions of the human brain, highlighting the alignment between the brain's hierarchical nature and hyperbolic geometry. By examining the brain's complex network of neuron connections and its cognitive processes, we illustrate how hyperbolic geometry plays a pivotal role in human intelligence. Empirical evidence indicates that hyperbolic neural networks outperform Euclidean models for tasks including natural language processing, computer vision and complex network analysis, requiring fewer parameters and exhibiting better generalisation. Despite its nascent adoption, hyperbolic geometry holds promise for improving machine learning models and advancing the field toward AGI.

Knowledge distillation (KD) methods can transfer knowledge of a parameter-heavy teacher model to a light-weight student model. The status quo for feature KD methods is to utilize loss functions based on logits (i.e., pre-softmax class scores) and intermediate layer features (i.e., latent representations). Unlike previous approaches, we propose a feature KD framework for training the student's backbone using feature-based losses exclusively (i.e., without logit-based losses such as cross entropy). Leveraging recent discoveries about the geometry of latent representations, we introduce a knowledge quality metric for identifying which teacher layers provide the most effective knowledge for distillation. Experiments on three image classification datasets with four diverse student-teacher pairs, spanning convolutional neural networks and vision transformers, demonstrate our KD method achieves state-of-the-art performance, delivering top-1 accuracy boosts of up to 15% over standard approaches. We publically share our code to facilitate future work at https://github.com/Thegolfingocto/KD_wo_CE.

Reconstruction-based unsupervised learning can fail in two opposing ways: a model may reconstruct anomalies too accurately or discard valid nominal variation. Using the Pursuit of Subspaces hypothesis, we characterize these failures through the meet, union, and join geometries induced by the nominal components. Excess learned range produces join blindness, while insufficient capacity produces meet preference and loss of nominal fidelity. We show that the compact nominal union is optimal among nominal faithful ranges and generally requires a nonlinear reconstruction map. Based on this geometry, we introduce Dynamic Push and Pull, which learns from controlled perturbations without anomaly labels, and nested manifold carving, which applies the same principle recursively in latent space. Experiments confirm the predicted changes in latent geometry across every tested Push and Pull configuration. The proposed methods improve reconstruction-based anomaly detection across standard benchmarks and unseen image degradations, while also improving pretrained ECG representations for downstream classification. These results connect reconstruction failures to identifiable geometric conditions and provide practical mechanisms for learning compact representations.

We study the problem of recovering low-dimensional latent geometry from a random geometric graph generated by noisy, high-dimensional data. Specifically, we analyze the performance of a spectral embedding algorithm on the Signal+Noise Graph Model, in which vertices are associated to points perturbed by Gaussian noise, and edges are included for pairs whose inner product exceeds a specified alignment threshold. In the high-dimensional regime where the number n of points and the ambient dimension d both tend to infinity, we show that under a spectral gap condition, the top eigenvectors and eigenvalues of the graph's adjacency matrix can be used to approximately recover the point cloud up to an orthogonal transformation. We illustrate our results on point clouds sampled from nested spheres and high-dimensional sinusoid curves.

State space models (SSM) have been widely applied for the analysis and visualization of large sequential datasets. Sequential Monte Carlo (SMC) is a very popular particle-based method to sample latent states from intractable posteriors. However, SSM is significantly influenced by the choice of the proposal. Recently Hamiltonian Monte Carlo (HMC) sampling has shown success in many practical problems. In this paper, we propose an SMC augmented by HMC (HSMC) for inference and model learning of nonlinear SSM, which can exempt us from learning proposals and reduce the model complexity significantly. Based on the measure preserving property of HMC, the particles directly generated by transition function can approximate the posterior of latent states arbitrarily well. In order to better adapt to the local geometry of latent space, the HMC is conducted on Riemannian manifold defined by a positive definite metric. In addition, we show that the proposed HSMC method can improve SSMs realized by both Gaussian Processes (GP) and Neural Network (NN).

Metric-induced discrete flow matching (MI-DFM) exploits token-latent geometry for discrete generation, but its practical use is limited by two issues: heuristic schedulers requiring hyperparameter search, and finite-step path-tracking error from its first-order continuous-time Markov chain (CTMC) solver. We address both issues. First, we derive a kinetic-optimal scheduler for prescribed scalar-parameterized probability paths, and instantiate it for MI-DFM as a training-free numerical schedule that traverses the path at constant Fisher-Rao speed. Second, we introduce a finite-step moment correction that adjusts the jump probability while preserving the CTMC jump destination distribution. We validate the resulting method, GibbsTTS, on codec-based zero-shot text-to-speech (TTS). Under controlled comparisons with a unified architecture and large-scale dataset, GibbsTTS achieves the best objective naturalness and is preferred in subjective evaluations over masked discrete generative baselines. Additionally, in comparison with the evaluated state-of-the-art TTS systems, GibbsTTS shows strong speaker similarity, achieving the highest similarity on three of four test sets and ranking second on the fourth. Project page: https://ydqmkkx.github.io/GibbsTTSProject

Generative modeling has shown increasing promise for predicting cellular perturbation effects under chemical compound treatments. Existing approaches either model perturbation as a distribution-to-distribution mapping without explicit concentration handling, or treat concentration as a discrete class label, precluding continuous dose control. We introduce a joint flow matching approach that simultaneously models cell latents and drug concentration via a dual-timestep formulation, enabling dose-conditioned single-cell morphing through the invertibility of flow matching. The joint formulation induces a monotonic dose-response geometry in latent space and additionally supports concentration estimation from cell morphology. As proof of concept, we further demonstrate generalization to an unseen dose held out during training. Empirically, our method achieves competitive or improved per-concentration metrics on two compounds compared with representative baselines, while enabling capabilities structurally unavailable to discrete-class methods.

We propose the Representation World Model (RWM), which learns states, transitions, and executable plans directly in representation space. Unlike existing world models that typically learn latent representations together with explicit dynamics models and perform planning through search, optimization, or policy-based prediction, RWM directly incorporates planning into the learned representation geometry. RWM learns the representation geometry by applying inverse-dynamics supervision locally along latent paths constructed from endpoint representations, requiring these paths to preserve task-relevant state and transition information. At inference, planning is performed by directly constructing a latent path between the current and goal representations, with inverse dynamics used to recover the corresponding actions, without recursive rollouts or action-space search. Experiments on continuous-control benchmarks demonstrate the effectiveness of RWM for direct planning, while results on robotic manipulation further show its potential to extend to more complex embodied control tasks. These results suggest that planning directly in representation space provides a promising alternative to conventional world-model planning.

Recent progress in generative modeling has made safety control a central challenge, yet existing approaches remain largely model-specific, requiring retraining or tailored interventions for each new architecture. In this work, we ask whether safety can be represented as a portable latent direction, learned once and reused across heterogeneous generators. We introduce the first framework for cross-model safety steering, in which a safety direction is estimated in a source LLM from paired safe-unsafe prompts, transported to a target generator through a lightweight alignment fitted on benign data alone, and applied at inference time. Crucially, our pipeline never accesses unsafe data on the target side, isolating whether safety can be transferred through shared representation geometry. Beyond a single global direction, we also identify a multi-vector extension that captures category-specific safety behaviors, enabling more selective control. We evaluate our approach in text-to-image and text-to-video generation across diverse source-target model pairs. Across models, transferred safety directions achieve ASR reduction and CLIP-Score/FID trade-offs comparable to directions learned natively on the target model using unsafe data, while requiring no target-side unsafe data. This indicates that safety improvements do not come at the expense of generation quality. Our results point to a modular view of safety: safety-relevant behavior is not purely model-local, but can be controlled through latent directions that persist across models. This suggests a new path toward lightweight, reusable safety mechanisms that do not require target-side unsafe data.

As AI foundation models grow in capability, a deeper question emerges: What shapes their internal cognitive identity -- beyond fluency and output? Benchmarks measure behavior, but the soul of a model resides in its latent geometry. In this work, we propose Neural DNA (nDNA) as a semantic-genotypic representation that captures this latent identity through the intrinsic geometry of belief. At its core, nDNA is synthesized from three principled and indispensable dimensions of latent geometry: spectral curvature, which reveals the curvature of conceptual flow across layers; thermodynamic length, which quantifies the semantic effort required to traverse representational transitions through layers; and belief vector field, which delineates the semantic torsion fields that guide a model's belief directional orientations. Like biological DNA, it encodes ancestry, mutation, and semantic inheritance, found in finetuning and alignment scars, cultural imprints, and architectural drift. In naming it, we open a new field: Neural Genomics, where models are not just tools, but digital semantic organisms with traceable inner cognition. Modeling statement. We read AI foundation models as semantic fluid dynamics: meaning is transported through layers like fluid in a shaped conduit; nDNA is the physics-grade readout of that flow -- a geometry-first measure of how meaning is bent, paid for, and pushed -- yielding a stable, coordinate-free neural DNA fingerprint tied to on-input behavior; with this fingerprint we cross into biology: tracing lineages across pretraining, fine-tuning, alignment, pruning, distillation, and merges; measuring inheritance between checkpoints; detecting drift as traits shift under new data or objectives; and, ultimately, studying the evolution of artificial cognition to compare models, diagnose risks, and govern change over time.

We present Clin-JEPA, a multi-phase co-training framework for joint-embedding predictive (JEPA) pretraining on EHR patient trajectories. JEPA architectures have enabled latent-space planning in robotics and high-quality representation learning in vision, but extending the paradigm to EHR data -- to obtain a single backbone that simultaneously forecasts patient trajectories and serves diverse downstream risk-prediction tasks without per-task fine-tuning -- remains an open challenge. Existing JEPA frameworks either discard the predictor after pretraining (I-JEPA, V-JEPA) or train it on a frozen pretrained encoder (V-JEPA 2-AC), leaving the encoder unaware of the rollout signal that the retained predictor must use at inference; co-training the encoder and predictor under a shared JEPA prediction objective would supply this grounding, but naïve co-training is unstable, with representation collapse and online/target drift causing autoregressive rollout to diverge. Clin-JEPA's five-phase pretraining curriculum -- predictor warmup, joint refinement, EMA target alignment, hard sync, and predictor finalization -- addresses each failure mode by phase, stably co-training a Qwen3-8B-based encoder and a 92M-parameter latent trajectory predictor. On MIMIC-IV ICU data, three independent evaluations support the framework: (1) latent ell_1 rollout drift uniquely converges (-15.7%) over 48-hour horizons while baselines and ablations diverge (+3% to +4951%); (2) the encoder learns a clinically discriminative latent geometry (deteriorating-patient cohorts displace 4.83times further than stable patients in latent space, vs leq2.62times for baseline encoders); (3) a single backbone outperforms strong tabular and sequence baselines on multi-task downstream evaluation. Clin-JEPA achieves mean AUROC 0.851 on ICareFM EEP and 0.883 on 8 binary risk tasks (+0.038 and +0.041 vs baseline average).

Masked reconstruction is widely used for EEG foundation models, but optimizing reconstruction on low-SNR waveforms does not necessarily produce the most useful latent representation. We introduce MANAS-2, a new EEG foundation model that combines a Raw-Band Hybrid (RBH) masked autoencoder with Constrained Reconstruction (ConRec), a physics-motivated regularizer. RBH jointly reconstructs temporal waveform patches and compact spectral-band targets, while ConRec acts only on the temporal decoder output, penalizing differences in RMS energy between adjacent short windows of the reconstructed waveform. ConRec is intended to shape the encoder by biasing it toward the organization of oscillatory-envelope information. Across seven held-out EEG datasets, adding ConRec to an otherwise identical RBH model increases frozen ridge recovery of six-band spectral power from mean R^2=0.860 to 0.906 and recovery of inter-patch band-energy dynamics from R^2=0.283 to 0.354, while temporal waveform information remains highly recoverable from the frozen latents. Applied to a temporal-only masked autoencoder, ConRec also improves frozen downstream transfer and frequency-dependent latent geometry despite receiving no spectral targets: i.e., the effects of ConRec are architecture-independent. MANAS-2 also outperforms leading EEG Foundation Models on most downstream knowledge-transfer tasks. From the effects of ConRec, we see that a physically motivated constraint imposed through the decoder can make for a more spectrally organized and transferable latent space. MANAS-2 therefore provides a new EEG foundation model built around constrained reconstruction as a mechanism for shaping representation--rather than reconstruction--quality.

Adversarial threats against LLMs are escalating faster than current defenses can adapt. We expose a critical geometric blind spot in alignment: adversarial prompts exploit latent camouflage, embedding perilously close to the safe representation manifold while encoding unsafe intent thereby evading surface level defenses like Direct Preference Optimization (DPO), which remain blind to the latent geometry. We introduce ALKALI, the first rigorously curated adversarial benchmark and the most comprehensive to date spanning 9,000 prompts across three macro categories, six subtypes, and fifteen attack families. Evaluation of 21 leading LLMs reveals alarmingly high Attack Success Rates (ASRs) across both open and closed source models, exposing an underlying vulnerability we term latent camouflage, a structural blind spot where adversarial completions mimic the latent geometry of safe ones. To mitigate this vulnerability, we introduce GRACE - Geometric Representation Aware Contrastive Enhancement, an alignment framework coupling preference learning with latent space regularization. GRACE enforces two constraints: latent separation between safe and adversarial completions, and adversarial cohesion among unsafe and jailbreak behaviors. These operate over layerwise pooled embeddings guided by a learned attention profile, reshaping internal geometry without modifying the base model, and achieve up to 39% ASR reduction. Moreover, we introduce AVQI, a geometry aware metric that quantifies latent alignment failure via cluster separation and compactness. AVQI reveals when unsafe completions mimic the geometry of safe ones, offering a principled lens into how models internally encode safety. We make the code publicly available at https://anonymous.4open.science/r/alkali-B416/README.md.

Diffusion-based image compression has recently shown outstanding perceptual fidelity, yet its practicality is hindered by prohibitive sampling overhead and high memory usage. Most existing diffusion codecs employ U-Net architectures, where hierarchical downsampling forces diffusion to operate in shallow latent spaces (typically with only 8x spatial downscaling), resulting in excessive computation. In contrast, conventional VAE-based codecs work in much deeper latent domains (16x - 64x downscaled), motivating a key question: Can diffusion operate effectively in such compact latent spaces without compromising reconstruction quality? To address this, we introduce DiT-IC, an Aligned Diffusion Transformer for Image Compression, which replaces the U-Net with a Diffusion Transformer capable of performing diffusion in latent space entirely at 32x downscaled resolution. DiT-IC adapts a pretrained text-to-image multi-step DiT into a single-step reconstruction model through three key alignment mechanisms: (1) a variance-guided reconstruction flow that adapts denoising strength to latent uncertainty for efficient reconstruction; (2) a self-distillation alignment that enforces consistency with encoder-defined latent geometry to enable one-step diffusion; and (3) a latent-conditioned guidance that replaces text prompts with semantically aligned latent conditions, enabling text-free inference. With these designs, DiT-IC achieves state-of-the-art perceptual quality while offering up to 30x faster decoding and drastically lower memory usage than existing diffusion-based codecs. Remarkably, it can reconstruct 2048x2048 images on a 16 GB laptop GPU.

Generative models and vision encoders have largely advanced on separate tracks, optimized for different goals and grounded in different mathematical principles. Yet, they share a fundamental property: latent space Gaussianity. Generative models map Gaussian noise to images, while encoders map images to semantic embeddings whose coordinates empirically behave as Gaussian. We hypothesize that both are views of a shared latent source, the Universal Normal Embedding (UNE): an approximately Gaussian latent space from which encoder embeddings and DDIM-inverted noise arise as noisy linear projections. To test our hypothesis, we introduce NoiseZoo, a dataset of per-image latents comprising DDIM-inverted diffusion noise and matching encoder representations (CLIP, DINO). On CelebA, linear probes in both spaces yield strong, aligned attribute predictions, indicating that generative noise encodes meaningful semantics along linear directions. These directions further enable faithful, controllable edits (e.g., smile, gender, age) without architectural changes, where simple orthogonalization mitigates spurious entanglements. Taken together, our results provide empirical support for the UNE hypothesis and reveal a shared Gaussian-like latent geometry that concretely links encoding and generation. Code and data are available https://rbetser.github.io/UNE/

World building with 3D scene representations is increasingly important for content creation, simulation, and interactive experiences, yet real workflows are inherently iterative: creators must repeatedly extend an existing scene under user control. Motivated by this research gap, we study 3D scene expansion in a user-centric workflow: starting from a real scene captured by multi-view images, we extend its coverage by inserting an additional view synthesized by a generative model. Unlike simple object editing or style transfer in a fixed scene, the inserted view is often 3D-misaligned with the original reconstruction, introducing geometry shifts, hallucinated content, or view-dependent artifacts that break global multi-view consistency. To address the challenge, we propose SceneExpander, which applies test-time adaptation to a parametric feed-forward 3D reconstruction model with two complementary distillation signals: anchor distillation stabilizes the original scene by distilling geometric cues from the captured views, while inserted-view self-distillation preserves observation-supported predictions yet adapts latent geometry and appearance to accommodate the misaligned inserted view. Experiments on ETH scenes and online data demonstrate improved expansion behavior and reconstruction quality under misalignment.

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep generative models. A key issue with these models is their tendency to output samples outside of the support of the target distribution when learning disconnected distributions. We investigate the relationship between the performance of these models and the geometry of their latent space. Building on recent developments in geometric measure theory, we prove a sufficient condition for optimality in the case where the dimension of the latent space is larger than the number of modes. Through experiments on GANs, we demonstrate the validity of our theoretical results and gain new insights into the latent space geometry of these models. Additionally, we propose a truncation method that enforces a simplicial cluster structure in the latent space and improves the performance of GANs.

High-fidelity 3D asset generation is crucial for various industries. While recent 3D pretrained models show strong capability in producing realistic content, most are built upon diffusion models and follow a two-stage pipeline that first generates geometry and then synthesizes appearance. Such a decoupled design tends to produce geometry-texture misalignment and non-negligible cost. In this paper, we propose UniLat3D, a unified framework that encodes geometry and appearance in a single latent space, enabling direct single-stage generation. Our key contribution is a geometry-appearance Unified VAE, which compresses high-resolution sparse features into a compact latent representation -- UniLat. UniLat integrates structural and visual information into a dense low-resolution latent, which can be efficiently decoded into diverse 3D formats, e.g., 3D Gaussians and meshes. Based on this unified representation, we train a single flow-matching model to map Gaussian noise directly into UniLat, eliminating redundant stages. Trained solely on public datasets, UniLat3D produces high-quality 3D assets in seconds from a single image, achieving superior appearance fidelity and geometric quality. More demos \& code are available at https://unilat3d.github.io/

Medical vision-language models enable co-learning and integrating features from medical imaging and clinical text. However, these models are not easy to train and the latent representation space can be complex. Here we propose a novel way for pre-training and regularising medical vision-language models. The proposed method, named Medical vision-language pre-training with Frozen language models and Latent spAce Geometry optimization (M-FLAG), leverages a frozen language model for training stability and efficiency and introduces a novel orthogonality loss to harmonize the latent space geometry. We demonstrate the potential of the pre-trained model on three downstream tasks: medical image classification, segmentation, and object detection. Extensive experiments across five public datasets demonstrate that M-FLAG significantly outperforms existing medical vision-language pre-training approaches and reduces the number of parameters by 78\%. Notably, M-FLAG achieves outstanding performance on the segmentation task while using only 1\% of the RSNA dataset, even outperforming ImageNet pre-trained models that have been fine-tuned using 100\% of the data.

We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces geodesics to decode as straight segments in data space, effectively ignoring any intrinsic data geometry beyond the ambient Euclidean space. Complementing this view, diffusion also admits a stochastic decoder via the reverse SDE, which enables an information geometric treatment with the Fisher-Rao metric. However, a choice of x_T as the latent representation collapses this metric due to memorylessness. We address this by introducing a latent spacetime z=(x_t,t) that indexes the family of denoising distributions p(x_0 | x_t) across all noise scales, yielding a nontrivial geometric structure. We prove these distributions form an exponential family and derive simulation-free estimators for curve lengths, enabling efficient geodesic computation. The resulting structure induces a principled Diffusion Edit Distance, where geodesics trace minimal sequences of noise and denoise edits between data. We also demonstrate benefits for transition path sampling in molecular systems, including constrained variants such as low-variance transitions and region avoidance. Code is available at: https://github.com/rafalkarczewski/spacetime-geometry.

We introduce BLARM, a feed-forward method for video-driven 3D mesh animation. Given a monocular video and a static object mesh, BLARM predicts a temporally coherent animated mesh whose motion follows the video. Rather than relying on explicit rigs or directly regressing high-dimensional vertex motion, we represent animation using a compact set of learned, time-varying rigid motion components and time-invariant vertex-to-component skinning weights. This yields a low-dimensional deformation space without requiring skeletons, cages, skinning weights, or rig annotations. Our architecture conditions geometry-derived deformation latents on video features through factorized spatial-temporal attention, then decodes rigid transformations blended by predicted skinning weights. Trained with trajectory reconstruction, entropy regularization, and motion-aware contrastive learning, BLARM produces accurate and temporally stable animations while recovering compact, interpretable motion structure from monocular video.

Generative autoencoders offer a promising approach for controllable text generation by leveraging their latent sentence representations. However, current models struggle to maintain coherent latent spaces required to perform meaningful text manipulations via latent vector operations. Specifically, we demonstrate by example that neural encoders do not necessarily map similar sentences to nearby latent vectors. A theoretical explanation for this phenomenon establishes that high capacity autoencoders can learn an arbitrary mapping between sequences and associated latent representations. To remedy this issue, we augment adversarial autoencoders with a denoising objective where original sentences are reconstructed from perturbed versions (referred to as DAAE). We prove that this simple modification guides the latent space geometry of the resulting model by encouraging the encoder to map similar texts to similar latent representations. In empirical comparisons with various types of autoencoders, our model provides the best trade-off between generation quality and reconstruction capacity. Moreover, the improved geometry of the DAAE latent space enables zero-shot text style transfer via simple latent vector arithmetic.

Latent action pretraining learns representations of visual change from pairs of observations, but existing methods typically encode each transition as a single unstructured representation that entangles transition extent and transition mode. We introduce Polar Latent Actions with Radial structure (PoLAR), which imposes a radial-direction structure on latent actions, encouraging radius to encode transition extent and direction to retain transition mode. PoLAR uses temporal offset between two observations as a weak proxy for transition extent, encouraging latent action from observation pairs separated by larger temporal gaps to occupy larger radii. We instantiate this structure in hyperbolic space, whose expanding volume with radius offers a natural fit for more diverse transition modes at larger extents. Across in-task and large-scale pretraining settings, PoLAR improves downstream policy performance in simulation and real-world robot experiments, outperforming latent action baselines and strong pretrained VLAs. These results suggest that the geometry of the latent action space is an important design choice for transferring visual pretraining to downstream robot policy learning.

Reliable uncertainty quantification is essential for deploying deep learning models in high-stakes settings, where out-of-distribution and adversarial inputs can induce confident but unreliable predictions. Evidential Deep Learning provides efficient uncertainty estimates in a single forward pass, but can still assign high evidential strength to inputs that are poorly supported by the learned representation, such as adversarial inputs. We introduce CLEAR, a lightweight, task-agnostic post-hoc method that improves evidential robustness without retraining or altering the base prediction. Using held-out calibration data, CLEAR characterises the group-conditioned geometry of the model's latent space. At inference, it efficiently generates perturbation views directly in the latent space and measures their conflict relative to the calibrated geometry of the predicted group. High latent conflict indicates unsupported evidence, which CLEAR uses to selectively reduce evidential strength while retaining evidence for latent-consistent inputs. On ImageNetrightarrowCUB, CLEAR improves OOD and adversarial AUROC by +8.29 and +5.01 while running 17.4times faster than competing post-hoc methods while preserving predictive performance across classification, regression, and object detection benchmarks.

Despite recent successes in hair acquisition that fits a high-dimensional hair model to a specific input subject, generative hair models, which establish general embedding spaces for encoding, editing, and sampling diverse hairstyles, are way less explored. In this paper, we present GroomGen, the first generative model designed for hair geometry composed of highly-detailed dense strands. Our approach is motivated by two key ideas. First, we construct hair latent spaces covering both individual strands and hairstyles. The latent spaces are compact, expressive, and well-constrained for high-quality and diverse sampling. Second, we adopt a hierarchical hair representation that parameterizes a complete hair model to three levels: single strands, sparse guide hairs, and complete dense hairs. This representation is critical to the compactness of latent spaces, the robustness of training, and the efficiency of inference. Based on this hierarchical latent representation, our proposed pipeline consists of a strand-VAE and a hairstyle-VAE that encode an individual strand and a set of guide hairs to their respective latent spaces, and a hybrid densification step that populates sparse guide hairs to a dense hair model. GroomGen not only enables novel hairstyle sampling and plausible hairstyle interpolation, but also supports interactive editing of complex hairstyles, or can serve as strong data-driven prior for hairstyle reconstruction from images. We demonstrate the superiority of our approach with qualitative examples of diverse sampled hairstyles and quantitative evaluation of generation quality regarding every single component and the entire pipeline.

We introduce Z-SASLM, a Zero-Shot Style-Aligned SLI (Spherical Linear Interpolation) Blending Latent Manipulation pipeline that overcomes the limitations of current multi-style blending methods. Conventional approaches rely on linear blending, assuming a flat latent space leading to suboptimal results when integrating multiple reference styles. In contrast, our framework leverages the non-linear geometry of the latent space by using SLI Blending to combine weighted style representations. By interpolating along the geodesic on the hypersphere, Z-SASLM preserves the intrinsic structure of the latent space, ensuring high-fidelity and coherent blending of diverse styles - all without the need for fine-tuning. We further propose a new metric, Weighted Multi-Style DINO ViT-B/8, designed to quantitatively evaluate the consistency of the blended styles. While our primary focus is on the theoretical and practical advantages of SLI Blending for style manipulation, we also demonstrate its effectiveness in a multi-modal content fusion setting through comprehensive experimental studies. Experimental results show that Z-SASLM achieves enhanced and robust style alignment. The implementation code can be found at: https://github.com/alessioborgi/Z-SASLM.

Reconstructing dynamic 3D scenes (i.e., 4D geometry) from monocular video is an important yet challenging problem. Conventional multiview geometry-based approaches often struggle with dynamic motion, whereas recent learning-based methods either require specialized 4D representation or sophisticated optimization. In this paper, we present Sora3R, a novel framework that taps into the rich spatiotemporal priors of large-scale video diffusion models to directly infer 4D pointmaps from casual videos. Sora3R follows a two-stage pipeline: (1) we adapt a pointmap VAE from a pretrained video VAE, ensuring compatibility between the geometry and video latent spaces; (2) we finetune a diffusion backbone in combined video and pointmap latent space to generate coherent 4D pointmaps for every frame. Sora3R operates in a fully feedforward manner, requiring no external modules (e.g., depth, optical flow, or segmentation) or iterative global alignment. Extensive experiments demonstrate that Sora3R reliably recovers both camera poses and detailed scene geometry, achieving performance on par with state-of-the-art methods for dynamic 4D reconstruction across diverse scenarios.

The discovery of the disentanglement properties of the latent space in GANs motivated a lot of research to find the semantically meaningful directions on it. In this paper, we suggest that the disentanglement property is closely related to the geometry of the latent space. In this regard, we propose an unsupervised method for finding the semantic-factorizing directions on the intermediate latent space of GANs based on the local geometry. Intuitively, our proposed method, called Local Basis, finds the principal variation of the latent space in the neighborhood of the base latent variable. Experimental results show that the local principal variation corresponds to the semantic factorization and traversing along it provides strong robustness to image traversal. Moreover, we suggest an explanation for the limited success in finding the global traversal directions in the latent space, especially W-space of StyleGAN2. We show that W-space is warped globally by comparing the local geometry, discovered from Local Basis, through the metric on Grassmannian Manifold. The global warpage implies that the latent space is not well-aligned globally and therefore the global traversal directions are bound to show limited success on it.

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.

Free-moving object reconstruction from monocular video remains challenging, particularly without reliable pose or depth cues and under arbitrary object motion. We introduce OnlineSplatter, a novel online feed-forward framework generating high-quality, object-centric 3D Gaussians directly from RGB frames without requiring camera pose, depth priors, or bundle optimization. Our approach anchors reconstruction using the first frame and progressively refines the object representation through a dense Gaussian primitive field, maintaining constant computational cost regardless of video sequence length. Our core contribution is a dual-key memory module combining latent appearance-geometry keys with explicit directional keys, robustly fusing current frame features with temporally aggregated object states. This design enables effective handling of free-moving objects via spatial-guided memory readout and an efficient sparsification mechanism, ensuring comprehensive yet compact object coverage. Evaluations on real-world datasets demonstrate that OnlineSplatter significantly outperforms state-of-the-art pose-free reconstruction baselines, consistently improving with more observations while maintaining constant memory and runtime.

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

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural operators have emerged as a promising technique to solve elliptic PDEs more efficiently by directly mapping the input to solutions. However, existing networks typically cannot handle complex geometries and inhomogeneous boundary values present in the real world. Here we introduce Boundary-Embedded Neural Operators (BENO), a novel neural operator architecture that embeds the complex geometries and inhomogeneous boundary values into the solving of elliptic PDEs. Inspired by classical Green's function, BENO consists of two branches of Graph Neural Networks (GNNs) for interior source term and boundary values, respectively. Furthermore, a Transformer encoder maps the global boundary geometry into a latent vector which influences each message passing layer of the GNNs. We test our model extensively in elliptic PDEs with various boundary conditions. We show that all existing baseline methods fail to learn the solution operator. In contrast, our model, endowed with boundary-embedded architecture, outperforms state-of-the-art neural operators and strong baselines by an average of 60.96\%. Our source code can be found https://github.com/AI4Science-WestlakeU/beno.git.

Learning, at its core, extends beyond memorization to the ability to reason and solve novel problems by navigating a space of possibilities. We introduce Lumo-2, a latent world-action model that generates actions by reasoning over world dynamics in latent space. The learned latent world dynamics capture physically grounded visual transitions, naturally encoding future possibilities and providing a unified substrate for cross-modal alignment. This formulation enables predictive reasoning akin to world modelling while remaining lightweight and focused on physical dynamics relevant to control. Central to our approach is the hypothesis that action generation quality is governed by the geometry of the latent space. We observe that standard reconstruction-based action tokenization objectives induce representations biased toward low-level signal fidelity, leading to misalignment between reconstruction quality and downstream control performance. To address this limitation, we propose a multi-stage modality pre-alignment strategy in which action representations are progressively aligned with latent world dynamics, vision, and language. This process enforces cross-modal consistency, promotes abstraction, and induces a structured latent space for predictive reasoning. We provide a systematic empirical study of latent world modelling and modality alignment, analyzing their roles in scaling laws and out-of-distribution generalization. Results show that Lumo-2 consistently outperforms strong vision-language-action (VLA) and world-action model (WAM) baselines, with gains on challenging real-world tasks requiring temporal reasoning, physical understanding, or high control complexity, including long-horizon and dexterous manipulation. These findings suggest that structured multimodal alignment and predictive reasoning are fundamental principles for advancing embodied intelligence.

Feed-forward 3D Gaussian Splatting (3DGS) reconstructs a scene in a single forward pass, replacing per-scene optimization with a network trained across many scenes. Its quality, however, degrades sharply as the number of input images drops. The bottleneck is upstream of the reconstruction heads: from a few unposed views, the internal representation they read carries no evidence for unobserved regions, leaving holes, floaters, and blur. The common remedy supplies that evidence as pixels, synthesizing extra views with an image or video generator and re-encoding them, which is costly and not 3D-consistent by construction. We instead densify the evidence itself. We present DensiTok, a plug-in module for pretrained feed-forward 3DGS models that densifies their internal geometry tokens directly, making a frozen backbone behave as though it had observed many more views than it was given. DensiTok compresses those tokens into a compact latent space, completes the latents of the unobserved viewpoints in a single flow-matching step conditioned on camera geometry, and decodes them back into tokens that the original reconstruction heads. The same module design can be integrated into different pretrained predictors while keeping each backbone and its reconstruction heads frozen. Completion in a low-dimensional latent space requires no image synthesis or additional encoder passes. Across three pretrained backbones and two benchmarks, DensiTok consistently improves sparse-view reconstruction and recovers much of the gap to dense-view reconstruction.

In this paper, we present Surf-D, a novel method for generating high-quality 3D shapes as Surfaces with arbitrary topologies using Diffusion models. Specifically, we adopt Unsigned Distance Field (UDF) as the surface representation, as it excels in handling arbitrary topologies, enabling the generation of complex shapes. While the prior methods explored shape generation with different representations, they suffer from limited topologies and geometry details. Moreover, it's non-trivial to directly extend prior diffusion models to UDF because they lack spatial continuity due to the discrete volume structure. However, UDF requires accurate gradients for mesh extraction and learning. To tackle the issues, we first leverage a point-based auto-encoder to learn a compact latent space, which supports gradient querying for any input point through differentiation to effectively capture intricate geometry at a high resolution. Since the learning difficulty for various shapes can differ, a curriculum learning strategy is employed to efficiently embed various surfaces, enhancing the whole embedding process. With pretrained shape latent space, we employ a latent diffusion model to acquire the distribution of various shapes. Our approach demonstrates superior performance in shape generation across multiple modalities and conducts extensive experiments in unconditional generation, category conditional generation, 3D reconstruction from images, and text-to-shape tasks.

Multimodal models have demonstrated powerful capabilities in complex tasks requiring multimodal alignment including zero-shot classification and cross-modal retrieval. However, existing models typically rely on millions of paired multimodal samples, which are prohibitively expensive or infeasible to obtain in many domains. In this work, we explore the feasibility of building multimodal models with limited amount of paired data by aligning pretrained unimodal foundation models. We show that high-quality alignment is possible with as few as tens of thousands of paired samplesx2013less than 1% of the data typically used in the field. To achieve this, we introduce STRUCTURE, an effective regularization technique that preserves the neighborhood geometry of the latent space of unimodal encoders. Additionally, we show that aligning last layers is often suboptimal and demonstrate the benefits of aligning the layers with the highest representational similarity across modalities. These two components can be readily incorporated into existing alignment methods, yielding substantial gains across 24 zero-shot image classification and retrieval benchmarks, with average relative improvement of 51.6% in classification and 91.8% in retrieval tasks. Our results highlight the effectiveness and broad applicability of our framework for limited-sample multimodal learning and offer a promising path forward for resource-constrained domains.

We propose CRAFT, a red-teaming alignment framework that leverages model reasoning capabilities and hidden representations to improve robustness against jailbreak attacks. Unlike prior defenses that operate primarily at the output level, CRAFT aligns large reasoning models to generate safety-aware reasoning traces by explicitly optimizing objectives defined over the hidden state space. Methodologically, CRAFT integrates contrastive representation learning with reinforcement learning to separate safe and unsafe reasoning trajectories, yielding a latent-space geometry that supports robust, reasoning-level safety alignment. Theoretically, we show that incorporating latent-textual consistency into GRPO eliminates superficially aligned policies by ruling them out as local optima. Empirically, we evaluate CRAFT on multiple safety benchmarks using two strong reasoning models, Qwen3-4B-Thinking and R1-Distill-Llama-8B, where it consistently outperforms state-of-the-art defenses such as IPO and SafeKey. Notably, CRAFT delivers an average 79.0% improvement in reasoning safety and 87.7% improvement in final-response safety over the base models, demonstrating the effectiveness of hidden-space reasoning alignment.

Despite the remarkable prowess of Vision-Language Models (VLMs) in general multimodal tasks, they remain fundamentally ``flat'' when reasoning about the physical world. We argue that this spatial bottleneck stems from a profound dimensional mismatch: while VLMs are trained to interpret 2D projections, true spatial reasoning demands the recovery of latent 3D geometry and temporal continuity. To conquer this high-dimensional complexity, we advocate a shift from monolithic learning to a ``divide and conquer'' paradigm. We present FactoSR, a factorized reinforcement learning framework that explicitly interpret the dimensions collapsed by visual projection. At its core, FactoSR decomposes the monolithic problem of world-consistent reasoning into three orthogonal, geometric sub-objectives: planar correspondence (XY), depth consistency (Z), and temporal reversibility (T). By optimizing these verifiable constraints within a unified policy learning mechanism, we effectively transform an ill-posed projection recovery problem into a series of tangible reasoning steps. Extensive evaluations on multi-view and video benchmarks demonstrate that this elegant decomposition yields substantial gains in 3D and 4D reasoning, achieving a 5.9% boost on VSI-Bench and 4.5% on All-Angles-Bench. Our findings suggest that reinforcing explicit, factorized 4D consistency is a critical step toward evolving VLMs into robust, world-aware reasoners.

Weather Jiu-Jitsu is a control paradigm for extreme climatological events, inspired by chaos theory. As a proposition, small, precise, targeted, and cost-inexpensive perturbations can redirect trajectories of a large dynamical system. This strategy has been demonstrated analytically in the Lorenz-63 system, where a naturally chaotic trajectory switching between two attractors can be confined to a single attractor, indefinitely, via arbitrarily small perturbations. This paper examines the feasibility of Microsoft's Aurora -- a 1.3 billion parameter global atmospheric model -- as a test bed for this strategy. This paper explores three questions: (1) Is Aurora a reliable enough simulation environment to serve as a meaningful testbed? (2) Are the perturbations required to redirect its trajectories small enough to be physically plausible? (3) Does Aurora's learned latent space (the parametric estimators on climatological attributes) yield any apparent, structured, and/or perhaps interpretable features that can convey a geo/atmospheric response to initial conditions? We find evidence consistent with all three: Aurora's modeled trajectories respond to perturbations beyond measurement drift, the perturbation magnitudes required are small relative to the model's own forecast uncertainty, and its latent representations exhibit directional structure that responds to Jiu-Jitsu-type interventions, even though that structure does not separate extreme from normal states outright. These results should be read as feasibility diagnostics rather than a demonstration of control: we do not implement or test an actual steering intervention on Aurora, and several of our findings, particularly around the model's latent-space geometry, are exploratory.

In this paper, we introduce Geometry-Inverse-Meet-Pixel-Insert, short for GEO, an exceptionally versatile image editing technique designed to cater to customized user requirements at both local and global scales. Our approach seamlessly integrates text prompts and image prompts to yield diverse and precise editing outcomes. Notably, our method operates without the need for training and is driven by two key contributions: (i) a novel geometric accumulation loss that enhances DDIM inversion to faithfully preserve pixel space geometry and layout, and (ii) an innovative boosted image prompt technique that combines pixel-level editing for text-only inversion with latent space geometry guidance for standard classifier-free reversion. Leveraging the publicly available Stable Diffusion model, our approach undergoes extensive evaluation across various image types and challenging prompt editing scenarios, consistently delivering high-fidelity editing results for real images.

While recent advances in generative latent spaces have driven substantial progress in single-image generation, the optimal latent space for novel view synthesis (NVS) remains largely unexplored. In particular, NVS requires geometrically consistent generation across viewpoints, but existing approaches typically operate in a view-independent VAE latent space. In this paper, we propose Geometric Latent Diffusion (GLD), a framework that repurposes the geometrically consistent feature space of geometric foundation models as the latent space for multi-view diffusion. We show that these features not only support high-fidelity RGB reconstruction but also encode strong cross-view geometric correspondences, providing a well-suited latent space for NVS. Our experiments demonstrate that GLD outperforms both VAE and RAE on 2D image quality and 3D consistency metrics, while accelerating training by more than 4.4x compared to the VAE latent space. Notably, GLD remains competitive with state-of-the-art methods that leverage large-scale text-to-image pretraining, despite training its diffusion model from scratch without such generative pretraining.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

Text-guided image generation has progressed rapidly in recent years, inspiring major breakthroughs in text-guided shape generation. Recently, it has been shown that using score distillation, one can successfully text-guide a NeRF model to generate a 3D object. We adapt the score distillation to the publicly available, and computationally efficient, Latent Diffusion Models, which apply the entire diffusion process in a compact latent space of a pretrained autoencoder. As NeRFs operate in image space, a naive solution for guiding them with latent score distillation would require encoding to the latent space at each guidance step. Instead, we propose to bring the NeRF to the latent space, resulting in a Latent-NeRF. Analyzing our Latent-NeRF, we show that while Text-to-3D models can generate impressive results, they are inherently unconstrained and may lack the ability to guide or enforce a specific 3D structure. To assist and direct the 3D generation, we propose to guide our Latent-NeRF using a Sketch-Shape: an abstract geometry that defines the coarse structure of the desired object. Then, we present means to integrate such a constraint directly into a Latent-NeRF. This unique combination of text and shape guidance allows for increased control over the generation process. We also show that latent score distillation can be successfully applied directly on 3D meshes. This allows for generating high-quality textures on a given geometry. Our experiments validate the power of our different forms of guidance and the efficiency of using latent rendering. Implementation is available at https://github.com/eladrich/latent-nerf

We introduce Orchid, a unified latent diffusion model that learns a joint appearance-geometry prior to generate color, depth, and surface normal images in a single diffusion process. This unified approach is more efficient and coherent than current pipelines that use separate models for appearance and geometry. Orchid is versatile - it directly generates color, depth, and normal images from text, supports joint monocular depth and normal estimation with color-conditioned finetuning, and seamlessly inpaints large 3D regions by sampling from the joint distribution. It leverages a novel Variational Autoencoder (VAE) that jointly encodes RGB, relative depth, and surface normals into a shared latent space, combined with a latent diffusion model that denoises these latents. Our extensive experiments demonstrate that Orchid delivers competitive performance against SOTA task-specific methods for geometry prediction, even surpassing them in normal-prediction accuracy and depth-normal consistency. It also inpaints color-depth-normal images jointly, with more qualitative realism than existing multi-step methods.

Neural signed distance functions (SDFs) have been a vital representation to represent 3D shapes or scenes with neural networks. An SDF is an implicit function that can query signed distances at specific coordinates for recovering a 3D surface. Although implicit functions work well on a single shape or scene, they pose obstacles when analyzing multiple SDFs with high-fidelity geometry details, due to the limited information encoded in the latent space for SDFs and the loss of geometry details. To overcome these obstacles, we introduce a method to represent multiple SDFs in a common space, aiming to recover more high-fidelity geometry details with more compact latent representations. Our key idea is to take full advantage of the benefits of generalization-based and overfitting-based learning strategies, which manage to preserve high-fidelity geometry details with compact latent codes. Based on this framework, we also introduce a novel sampling strategy to sample training queries. The sampling can improve the training efficiency and eliminate artifacts caused by the influence of other SDFs. We report numerical and visual evaluations on widely used benchmarks to validate our designs and show advantages over the latest methods in terms of the representative ability and compactness.

Metamaterials are artificially engineered structures whose mechanical and physical behaviors are strongly shaped by geometry rather than composition. Voxel representation provides a unified format for metamaterial geometry generation, as it can express diverse classes such as truss, shell, and porous structures within a single cubic discretization. However, voxel-based generation faces a plausibility-novelty trade-off: staying close to known geometries helps preserve geometric regularities, while moving away from them is necessary for novelty but may produce degenerate geometries. To address this challenge, we propose REGDIFF, a generative framework that couples voxel representation with latent space regulation and guided diffusion. REGDIFF introduces a repel-and-sink (RAS) mechanism to smooth the latent distribution of plausible geometries, and short-range repulsion (SRR) guidance to discourage generation overly close to known samples while maintaining geometric plausibility. We further contribute a voxel-based benchmark covering truss- and shell-type metamaterial geometries, together with an evaluation module for geometric plausibility, novelty, and diversity. Experiments show that REGDIFF outperforms voxel-based generative baselines, achieving +8.9% in geometric plausibility, +46.4% in novelty, and +128.6% in diversity on average across two datasets. These results suggest that REGDIFF is a strong geometry candidate generator for downstream evaluation. Our code is provided at https://github.com/wzhan24/ReGDiff.

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.

Generative models, especially diffusion models (DMs), have achieved promising results for generating feature-rich geometries and advancing foundational science problems such as molecule design. Inspired by the recent huge success of Stable (latent) Diffusion models, we propose a novel and principled method for 3D molecule generation named Geometric Latent Diffusion Models (GeoLDM). GeoLDM is the first latent DM model for the molecular geometry domain, composed of autoencoders encoding structures into continuous latent codes and DMs operating in the latent space. Our key innovation is that for modeling the 3D molecular geometries, we capture its critical roto-translational equivariance constraints by building a point-structured latent space with both invariant scalars and equivariant tensors. Extensive experiments demonstrate that GeoLDM can consistently achieve better performance on multiple molecule generation benchmarks, with up to 7\% improvement for the valid percentage of large biomolecules. Results also demonstrate GeoLDM's higher capacity for controllable generation thanks to the latent modeling. Code is provided at https://github.com/MinkaiXu/GeoLDM.

The inductive bias of a graph neural network (GNN) is largely encoded in its specified graph. Latent graph inference relies on latent geometric representations to dynamically rewire or infer a GNN's graph to maximize the GNN's predictive downstream performance, but it lacks solid theoretical foundations in terms of embedding-based representation guarantees. This paper addresses this issue by introducing a trainable deep learning architecture, coined neural snowflake, that can adaptively implement fractal-like metrics on R^d. We prove that any given finite weights graph can be isometrically embedded by a standard MLP encoder. Furthermore, when the latent graph can be represented in the feature space of a sufficiently regular kernel, we show that the combined neural snowflake and MLP encoder do not succumb to the curse of dimensionality by using only a low-degree polynomial number of parameters in the number of nodes. This implementation enables a low-dimensional isometric embedding of the latent graph. We conduct synthetic experiments to demonstrate the superior metric learning capabilities of neural snowflakes when compared to more familiar spaces like Euclidean space. Additionally, we carry out latent graph inference experiments on graph benchmarks. Consistently, the neural snowflake model achieves predictive performance that either matches or surpasses that of the state-of-the-art latent graph inference models. Importantly, this performance improvement is achieved without requiring random search for optimal latent geometry. Instead, the neural snowflake model achieves this enhancement in a differentiable manner.

Large language models solve complex problems by generating lengthy chains of explicit reasoning tokens. While effective, this makes reasoning expensive, length-sensitive, and constrained to (discrete) natural language. While latent reasoning offers a continuous alternative, determining useful structures for intermediate latent states is an open challenge. In this paper, we formulate latent reasoning as a geometric path-approximation problem within the model's pretrained token-embedding space. We introduce Geometric Latent Reasoning (GLR), which uses a lightweight transition head to predict iterative direction updates in embedding space. Using textual chain-of-thought traces as anchors, GLR learns to approximate discrete reasoning trajectories while permitting continuous deviations from exact token embeddings. Evaluations on mathematical reasoning benchmarks using Qwen3 models reveal an emergent phenomenon: geometric latent reasoning induces substantially shorter generations without an explicit length objective. By replacing early explicit reasoning with continuous latent steps, models often reach correct answers using substantially fewer total generation steps. These findings suggest that continuous trajectories act as compact intermediate reasoning states, exposing a new tradeoff between latent computation budget, output length, and accuracy.

The latent space of diffusion model mostly still remains unexplored, despite its great success and potential in the field of generative modeling. In fact, the latent space of existing diffusion models are entangled, with a distorted mapping from its latent space to image space. To tackle this problem, we present Isometric Diffusion, equipping a diffusion model with a geometric regularizer to guide the model to learn a geometrically sound latent space of the training data manifold. This approach allows diffusion models to learn a more disentangled latent space, which enables smoother interpolation, more accurate inversion, and more precise control over attributes directly in the latent space. Our extensive experiments consisting of image interpolations, image inversions, and linear editing show the effectiveness of our method.

We propose a 3D latent representation that jointly models object geometry and view-dependent appearance. Most prior works focus on either reconstructing 3D geometry or predicting view-independent diffuse appearance, and thus struggle to capture realistic view-dependent effects. Our approach leverages that RGB-depth images provide samples of a surface light field. By encoding random subsamples of this surface light field into a compact set of latent vectors, our model learns to represent both geometry and appearance within a unified 3D latent space. This representation reproduces view-dependent effects such as specular highlights and Fresnel reflections under complex lighting. We further train a latent flow matching model on this representation to learn its distribution conditioned on a single input image, enabling the generation of 3D objects with appearances consistent with the lighting and materials in the input. Experiments show that our approach achieves higher visual quality and better input fidelity than existing methods.

Recent video world models have increasingly adopted 3D memory mechanisms to integrate historical observations into a lightweight and persistent scene representation. This naturally raises a complementary question: if 3D representations can serve as an effective mechanism for memorizing observed scenes, can they also be directly used as the latent space for reconstructing and generating scenes? Motivated by this idea, we represent a scene as a compact and unstructured 3D-anchored latent space (SceneAE). Each latent combines an explicit 3D position with an implicit content feature and is spatially grounded to describe its local scene region, forming a sparse latent point cloud. Unlike conventional video-VAE latents that describe how a scene appears from particular viewpoints, our representation directly describes the scene itself, making it naturally applicable to both reconstruction and generation. For reconstruction, once the scene has been generated, our persistent 3D representation can be projected and decoded into RGB-D observations by different target cameras, without the need to regenerate a video for each new camera trajectory. For generation, we leverage the geometry-content separation to first generate camera-controlled 3D geometry and then synthesize content conditioned on it, reducing camera-appearance entanglement and improving camera controllability. Experiments show that this 3D latent achieves superior generation quality, computational cost, and camera controllability.

Mathematical reasoning is a hallmark of human intelligence, requiring logical deduction, symbolic manipulation, and abstract thinking. Recent multimodal large language models (MLLMs) have demonstrated strong performance on geometry problems through multi-step reasoning. To better emulate human problem-solving, intermediate steps can incorporate auxiliary visual constructions, such as additional lines or points, which improve geometric interpretation and educational clarity. In this work, we introduce the GeoMathCode, where programmatic representations serve as intermediate visual outputs. We further conduct an in-depth analysis of the underlying reasoning geometry. Experimental results show that reasoning and code generation steps can be disentangled in the latent space, while supervised fine-tuning (SFT) makes the reasoning manifold more structured and informative. Moreover, hierarchical syntactic code structures emerge as disentangled latent subspaces, and contain more mathematical symbolic information than visual representations.

We propose a new representation for encoding 3D shapes as neural fields. The representation is designed to be compatible with the transformer architecture and to benefit both shape reconstruction and shape generation. Existing works on neural fields are grid-based representations with latents defined on a regular grid. In contrast, we define latents on irregular grids, enabling our representation to be sparse and adaptive. In the context of shape reconstruction from point clouds, our shape representation built on irregular grids improves upon grid-based methods in terms of reconstruction accuracy. For shape generation, our representation promotes high-quality shape generation using auto-regressive probabilistic models. We show different applications that improve over the current state of the art. First, we show results for probabilistic shape reconstruction from a single higher resolution image. Second, we train a probabilistic model conditioned on very low resolution images. Third, we apply our model to category-conditioned generation. All probabilistic experiments confirm that we are able to generate detailed and high quality shapes to yield the new state of the art in generative 3D shape modeling.

We propose ArtiLatent, a generative framework that synthesizes human-made 3D objects with fine-grained geometry, accurate articulation, and realistic appearance. Our approach jointly models part geometry and articulation dynamics by embedding sparse voxel representations and associated articulation properties, including joint type, axis, origin, range, and part category, into a unified latent space via a variational autoencoder. A latent diffusion model is then trained over this space to enable diverse yet physically plausible sampling. To reconstruct photorealistic 3D shapes, we introduce an articulation-aware Gaussian decoder that accounts for articulation-dependent visibility changes (e.g., revealing the interior of a drawer when opened). By conditioning appearance decoding on articulation state, our method assigns plausible texture features to regions that are typically occluded in static poses, significantly improving visual realism across articulation configurations. Extensive experiments on furniture-like objects from PartNet-Mobility and ACD datasets demonstrate that ArtiLatent outperforms existing approaches in geometric consistency and appearance fidelity. Our framework provides a scalable solution for articulated 3D object synthesis and manipulation.

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

Latent diffusion models have established a new state-of-the-art in high-resolution visual generation. Integrating Vision Foundation Model priors improves generative efficiency, yet existing latent designs remain largely heuristic. These approaches often struggle to unify semantic discriminability, reconstruction fidelity, and latent compactness. In this paper, we propose Geometric Autoencoder (GAE), a principled framework that systematically addresses these challenges. By analyzing various alignment paradigms, GAE constructs an optimized low-dimensional semantic supervision target from VFMs to provide guidance for the autoencoder. Furthermore, we leverage latent normalization that replaces the restrictive KL-divergence of standard VAEs, enabling a more stable latent manifold specifically optimized for diffusion learning. To ensure robust reconstruction under high-intensity noise, GAE incorporates a dynamic noise sampling mechanism. Empirically, GAE achieves compelling performance on the ImageNet-1K 256 times 256 benchmark, reaching a gFID of 1.82 at only 80 epochs and 1.31 at 800 epochs without Classifier-Free Guidance, significantly surpassing existing state-of-the-art methods. Beyond generative quality, GAE establishes a superior equilibrium between compression, semantic depth and robust reconstruction stability. These results validate our design considerations, offering a promising paradigm for latent diffusion modeling. Code and models are publicly available at https://github.com/freezing-index/Geometric-Autoencoder-for-Diffusion-Models.

While 3D content generation has advanced significantly, existing methods still face challenges with input formats, latent space design, and output representations. This paper introduces a novel 3D generation framework that addresses these challenges, offering scalable, high-quality 3D generation with an interactive Point Cloud-structured Latent space. Our framework employs a Variational Autoencoder (VAE) with multi-view posed RGB-D(epth)-N(ormal) renderings as input, using a unique latent space design that preserves 3D shape information, and incorporates a cascaded latent diffusion model for improved shape-texture disentanglement. The proposed method, GaussianAnything, supports multi-modal conditional 3D generation, allowing for point cloud, caption, and single/multi-view image inputs. Notably, the newly proposed latent space naturally enables geometry-texture disentanglement, thus allowing 3D-aware editing. Experimental results demonstrate the effectiveness of our approach on multiple datasets, outperforming existing methods in both text- and image-conditioned 3D generation.

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.

Existing geometry-aware Multimodal Large Language Models (MLLMs) increasingly rely on external 3D encoders to provide structural priors, but executing these additional encoder paths at inference introduces substantial latency and computational overhead. We propose GeoThinker-F, an efficient framework that internalizes spatiotemporal perception by transforming causal MLLM hidden states into predictive latent world representations. Our key insight is that intermediate semantic representations contain sufficient information to predict useful representations of current geometry and future semantics, without requiring an exact reproduction of features from a dedicated 3D encoder. To realize this idea, GeoThinker-F adopts a decoupled two-stage training strategy. In the first stage, the MLLM backbone is frozen while lightweight Latent Frame Prediction (LFP) heads learn from an offline 3D geometry expert and next-frame semantic targets. In the second stage, the external expert is removed, and the model is jointly optimized to generate and selectively integrate its self-predicted priors through a specialized Spatial-Grounded Temporal (SGT) Fusion module. Extensive evaluations show that GeoThinker-F eliminates runtime dependence on external 3D geometry encoders while maintaining competitive performance across diverse spatial intelligence benchmarks. It achieves up to a 3.6times inference speedup, reducing latency from 1.45,s to 0.40,s while retaining strong spatial reasoning performance.

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold using geodesic-guided flows. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.

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/

LLMs for clinical decision support often fail under small but clinically meaningful input shifts such as masking a symptom or negating a finding, despite high performance on static benchmarks. These reasoning failures frequently go undetected by standard NLP metrics, which are insensitive to latent representation shifts that drive diagnosis instability. We propose a geometry-aware evaluation framework, LAPD (Latent Agentic Perturbation Diagnostics), which systematically probes the latent robustness of clinical LLMs under structured adversarial edits. Within this framework, we introduce Latent Diagnosis Flip Rate (LDFR), a model-agnostic diagnostic signal that captures representational instability when embeddings cross decision boundaries in PCA-reduced latent space. Clinical notes are generated using a structured prompting pipeline grounded in diagnostic reasoning, then perturbed along four axes: masking, negation, synonym replacement, and numeric variation to simulate common ambiguities and omissions. We compute LDFR across both foundation and clinical LLMs, finding that latent fragility emerges even under minimal surface-level changes. Finally, we validate our findings on 90 real clinical notes from the DiReCT benchmark (MIMIC-IV), confirming the generalizability of LDFR beyond synthetic settings. Our results reveal a persistent gap between surface robustness and semantic stability, underscoring the importance of geometry-aware auditing in safety-critical clinical AI.

Despite the recent success of multi-view diffusion models for text/image-based 3D asset generation, instruction-based editing of 3D assets lacks surprisingly far behind the quality of generation models. The main reason is that recent approaches using 2D priors suffer from view-inconsistent editing signals. Going beyond 2D prior distillation methods and multi-view editing strategies, we propose a training-free editing method that operates within the latent space of a native 3D diffusion model, allowing us to directly manipulate 3D geometry. We guide the edit synthesis by blending 3D attention maps from the generation with the source object. Coupled with geometry-aware regularization guidance, a spectral modulation strategy in the Fourier domain and a refinement step for 3D enhancement, our method outperforms previous 3D editing methods enabling high-fidelity, precise, and robust edits across a wide range of shapes and semantic manipulations.

Robust in-bed human pose estimation under blanket occlusion remains challenging due to the scarcity of reliable labeled training data for heavily covered poses. Existing approaches rely on multi-modal sensing or image-to-image translation frameworks that remain conditioned on visible source imagery, limiting scalability and pose diversity. In this work, we reformulate occlusion-aware augmentation as a geometry-conditioned generative modeling task. We conduct a systematic comparison of deterministic masking, unpaired translation, paired diffusion-based translation, and a proposed pose-conditioned Latent Diffusion Model (Pose-LDM). Unlike image-guided methods, Pose-LDM synthesizes blanket-covered images directly from skeletal keypoints, eliminating dependence on paired supervision and pixel-level source-image conditioning while enabling generation from arbitrary pose inputs. All augmentation strategies are evaluated through their impact on downstream pose estimation under a fixed backbone. Pose- LDM achieves the highest strict localization accuracy under severe occlusion while maintaining overall detection performance comparable to paired diffusion models, approaching the performance of fully supervised training. These results demonstrate that geometry-conditioned diffusion provides an effective and supervision-efficient pathway toward occlusion-robust inbed pose estimation without modifying the sensing pipeline. The code is available at: github.com/navidTerraNova/ GeoDiffPose.

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.

Joint-Embedding Predictive Architectures (JEPAs) are effective for images, video, and audio, yet deterministic JEPA-style latent prediction has not become a standard objective for text encoders. We argue that this gap reflects a mismatch between squared-error latent prediction and the conditional structure of language. The key requirement is conditional concentration: given a context and target location, the target representation should lie near a single meaningful point. Local image prediction often satisfies this through spatial continuity, whereas masked text can admit multiple valid token or span completions whose representations need not share a coherent center. We formalize this mismatch through three conditions---predictability, non-collapse, and low conditional variance---and show how their failure creates centroid degeneracy and collapse pressure in text. Matched I-JEPA and T-JEPA experiments reveal the predicted sequence: mutual-information saturation and elevated target variance precede train--validation instability, effective-rank degeneration, cosine collapse, and poor downstream transfer. The same pattern appears across five independent data seeds, indicating that it is not a sampling artifact. These results do not rule out predictive learning for language; they show that text-compatible JEPA objectives must preserve multiple plausible completions rather than compress them into a single latent point.

Reconstructing photorealistic and animatable 4D head avatars from a single portrait image remains a fundamental challenge in computer vision. While diffusion models have enabled remarkable progress in image and video generation for avatar reconstruction, existing methods primarily rely on 2D priors and struggle to achieve consistent 3D geometry. We propose a novel framework that leverages geometry-aware diffusion to learn strong geometry priors for high-fidelity head avatar reconstruction. Our approach jointly synthesizes portrait images and corresponding surface normals, while a pose-free expression encoder captures implicit expression representations. Both synthesized images and expression latents are incorporated into 3D Gaussian-based avatars, enabling photorealistic rendering with accurate geometry. Extensive experiments demonstrate that our method substantially outperforms state-of-the-art approaches in visual quality, expression fidelity, and cross-identity generalization, while supporting real-time rendering.

Firm characteristics are commonly represented as fixed vectors, even though evidence about firms' operations arrives as heterogeneous collections of articles reports. We study how distances between distributions of firm characteristics restrict systematic covariance. For given latent exposure laws, quadratic Wasserstein geometry yields sharp covariance endpoints over admissible couplings. Under a common randomized bi-Lipschitz characteristic-to-exposure map, bounded risk-coordinate slack, and a maintained return-covariance bridge, characteristic-side distance yields a conditional interval for the covariance ceiling. Greater separation then leaves less scope for aligned systematic exposures when these assumptions are tight, while a non-negative transport excess term records the gap between realized and maximum-covariance arrangements. The resulting envelope is scenario analysis rather than an expected-return, no-arbitrage, or identified structural model. Empirically, we proxy characteristic distributions with encoder-only language-model embeddings of financial news articles, disclosures, and analyst reports for Nasdaq firms over 2018-2022. In a dyadic regression with symmetric firm effects, greater pairwise article-embedding W2 distance is associated with weaker return co-movement: the coefficient is 1.920, with 95% interval [1.412, 2.468]. The estimate retains the same sign when returns are measured in a later window, although the feature construction is not point-in-time and the evidence remains reduced form.

Posing 3D characters is a fundamental task in computer graphics and vision. However, existing methods like auto-rigging and pose-conditioned generation often struggle with challenges such as inaccurate skinning weight prediction, topological imperfections, and poor pose conformance, limiting their robustness and generalizability. To overcome these limitations, we introduce Make-It-Poseable, a novel feed-forward framework that reformulates character posing as a latent-space transformation problem. Instead of deforming mesh vertices as in traditional pipelines, our method reconstructs the character in new poses by directly manipulating its latent representation. At the core of our method is a latent posing transformer that manipulates shape tokens based on skeletal motion. This process is facilitated by a dense pose representation for precise control. To ensure high-fidelity geometry and accommodate topological changes, we also introduce a latent-space supervision strategy and an adaptive completion module. Our method demonstrates superior performance in posing quality. It also naturally extends to 3D editing applications like part replacement and refinement.

Background: The deployment of personalized Large Language Models (LLMs) is currently constrained by the stability-plasticity dilemma. Prevailing alignment methods, such as Supervised Fine-Tuning (SFT), rely on stochastic weight updates that often incur an "alignment tax" -- degrading general reasoning capabilities. Methods: We propose the Soul Engine, a framework based on the Linear Representation Hypothesis, which posits that personality traits exist as orthogonal linear subspaces. We introduce SoulBench, a dataset constructed via dynamic contextual sampling. Using a dual-head architecture on a frozen Qwen-2.5 base, we extract disentangled personality vectors without modifying the backbone weights. Results: Our experiments demonstrate three breakthroughs. First, High-Precision Profiling: The model achieves a Mean Squared Error (MSE) of 0.011 against psychological ground truth. Second, Geometric Orthogonality: T-SNE visualization confirms that personality manifolds are distinct and continuous, allowing for "Zero-Shot Personality Injection" that maintains original model intelligence. Third, Deterministic Steering: We achieve robust control over behavior via vector arithmetic, validated through extensive ablation studies. Conclusion: This work challenges the necessity of fine-tuning for personalization. By transitioning from probabilistic prompting to deterministic latent intervention, we provide a mathematically rigorous foundation for safe, controllable AI personalization.

We introduce a framework for learning latent representations of 4D objects which are descriptive, faithfully capturing object geometry and appearance; compressive, aiding in downstream efficiency; and accessible, requiring minimal input, i.e., an unstructured dynamic point cloud, to construct. Specifically, Velox trains an encoder to compress spatiotemporal color point clouds into a set of dynamic shape tokens. These tokens are supervised using two complementary decoders: a 4D surface decoder, which models the time-varying surface distribution capturing the geometry; and a Gaussian decoder, which maps the tokens to 3D Gaussians, helping learn appearance. To demonstrate the utility of our representation, we evaluate it across three downstream tasks -- video-to-4D generation, 3D tracking, and cloth simulation via image-to-4D generation -- and observe strong performances in all settings.

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.

World Action Models (WAMs) couple action generation with prediction of future states. Their effectiveness depends on whether future dynamics are modeled in a space that is both aligned with action generation and sufficiently geometry-aware to capture where and how actions change the scene. Existing WAMs typically satisfy only part of this requirement, relying on either perceptually heavy observation-space targets or auxiliary latent spaces that are not jointly structured for action relevance and geometry. We propose SG-WAM, a self-guided framework that learns geometry-aware action-conditioned dynamics directly in the policy-derived representation space. SG-WAM introduces learnable dynamics tokens and a Self-Guided World Predictor that forecasts their future latent states conditioned on intervening robot actions. Prediction targets are generated by an exponential moving average copy of the same policy backbone, providing stable supervision within the representation family used by the action expert. Geometric supervision further structures the policy image-token representations, providing spatially grounded context for the dynamics tokens and yielding a future-alignment space that is both action-relevant and geometry-aware. Latent future prediction, geometric grounding, and flow-matching action generation are jointly optimized end-to-end in a unified framework. Built on a 0.9B model without large-scale embodied pretraining, SG-WAM achieves 98.5% average success on LIBERO and 73% on LIBERO-Plus, while outperforming strong baselines in both in-distribution and out-of-distribution real-world evaluations.

Latent action world models let agents plan new behaviors at test time by predicting how actions change the environment, and joint-embedding predictive architectures (JEPAs) do so by forecasting future latent states rather than pixels. Yet nearly all such models see the world through a camera, even though robotic manipulation is fundamentally geometric: in robotics goals for manipulation are traditionally specified by target object poses, not by images of the object once placed. We ask whether latent planning survives a shift from appearance to geometry, on the observation side as well as on the goal specifications side. To answer this, we extend the stable-worldmodel evaluation platform with simulated LiDAR-style raycast point clouds as a new sensor modality, and adapt three JEPA designs to point clouds: a frozen-encoder model built on Utonia features, a distribution-prior model based on LeWM, and an action-sensitive model based on Delta-JEPA. We further introduce a goal-encoding mechanism that constructs the goal latent from the current latent and a 3D target pose, removing the need for goal images or goal point clouds. A comparative evaluation of the different anti-collapse mechanisms shows that point-cloud world models can match their image-based counterparts, demonstrating that the modality shift from appearance to geometry is achievable. All models are released as open weights with open-source training and inference code, to make world-model planning accessible for LiDAR-driven and pose-directed robotic tasks.

Novel view synthesis from sparse images must reconcile faithful reconstruction of observed regions with plausible completion of unseen content, while maintaining world consistency across viewpoints. Existing geometry-based methods preserve observed scene structure but often struggle to complete unseen regions, whereas video generative models offer rich appearance priors but accumulate inconsistencies during sequential view generation. We propose GeoVerse, a framework that synthesizes world-consistent novel views by performing generation within the geometric latent space of a pretrained 3D foundation model and injecting appearance priors from a video generative model. Specifically, GeoVerse extracts multilevel features from Wan2.2 VACE and injects them into the geometric latent diffusion model via a ControlNet-style adapter, incorporating video-learned appearance priors to enhance structural completion. To enforce cross-view coherence, a global spatial memory continuously aggregates observed and synthesized content, reprojecting target-aligned guidance to anchor subsequent predictions to a shared scene representation. Extensive experiments across diverse datasets demonstrate improved visual quality and geometric consistency, with a 2.23 dB higher PSNR on DL3DV and 32.4% lower ATE on Mip-NeRF360 compared to GLD.

Image relighting is the task of showing what a scene from a source image would look like if illuminated differently. Inverse graphics schemes recover an explicit representation of geometry and a set of chosen intrinsics, then relight with some form of renderer. However error control for inverse graphics is difficult, and inverse graphics methods can represent only the effects of the chosen intrinsics. This paper describes a relighting method that is entirely data-driven, where intrinsics and lighting are each represented as latent variables. Our approach produces SOTA relightings of real scenes, as measured by standard metrics. We show that albedo can be recovered from our latent intrinsics without using any example albedos, and that the albedos recovered are competitive with SOTA methods.

This paper introduces a novel hierarchical autoencoder that maps 3D models into a highly compressed latent space. The hierarchical autoencoder is specifically designed to tackle the challenges arising from large-scale datasets and generative modeling using diffusion. Different from previous approaches that only work on a regular image or volume grid, our hierarchical autoencoder operates on unordered sets of vectors. Each level of the autoencoder controls different geometric levels of detail. We show that the model can be used to represent a wide range of 3D models while faithfully representing high-resolution geometry details. The training of the new architecture takes 0.70x time and 0.58x memory compared to the baseline. We also explore how the new representation can be used for generative modeling. Specifically, we propose a cascaded diffusion framework where each stage is conditioned on the previous stage. Our design extends existing cascaded designs for image and volume grids to vector sets.

Recent advances in Neural Fields have enabled powerful, discretization-invariant methods for learning neural operators that approximate solutions of Partial Differential Equations (PDEs) on general geometries. Building on these developments, we introduce enf2enf, an encoder--decoder methodology for predicting steady-state Partial Differential Equations with non-parameterized geometric variability, based on recently proposed Equivariant Neural Field architectures. In enf2enf, input geometries are encoded into latent point cloud embeddings that inherently preserve geometric grounding and capture local phenomena. The resulting representations are then combined with global parameters and directly decoded into continuous output fields, thus efficiently modeling the coupling between geometry and physics. By leveraging the inductive biases of locality and translation invariance, our approach is able to capture fine-scale physical features as well as complex shape variations, thereby enhancing generalization and physical compliance. Extensive experiments on a high-fidelity aerodynamic dataset, a hyper-elastic material benchmark, and multi-element airfoil geometries, demonstrate that the proposed model achieves superior or competitive performance compared to state-of-the-art graph based, operator learning, and neural field methods. Notably, our method supports real time inference and zero-shot super-resolution, enabling efficient training on low-resolution meshes while maintaining high accuracy on full-scale discretizations.

Monocular and stereo depth estimation offer complementary strengths: monocular methods capture rich contextual priors but lack geometric precision, while stereo approaches leverage epipolar geometry yet struggle with ambiguities such as reflective or textureless surfaces. Despite post-hoc synergies, these paradigms remain largely disjoint in practice. We introduce a unified framework that bridges both through iterative bidirectional alignment of their latent representations. At its core, a novel cross-attentive alignment mechanism dynamically synchronizes monocular contextual cues with stereo hypothesis representations during stereo reasoning. This mutual alignment resolves stereo ambiguities (e.g., specular surfaces) by injecting monocular structure priors while refining monocular depth with stereo geometry within a single network. Extensive experiments demonstrate state-of-the-art results: it reduces zero-shot generalization error by !>!40% on Middlebury and ETH3D, while addressing longstanding failures on transparent and reflective surfaces. By harmonizing multi-view geometry with monocular context, our approach enables robust 3D perception that transcends modality-specific limitations. Codes available at https://github.com/aeolusguan/BridgeDepth.

We introduce Representation Tokenizer (RepTok), a generative modeling framework that represents an image using a single continuous latent token obtained from self-supervised vision transformers. Building on a pre-trained SSL encoder, we fine-tune only the semantic token embedding and pair it with a generative decoder trained jointly using a standard flow matching objective. This adaptation enriches the token with low-level, reconstruction-relevant details, enabling faithful image reconstruction. To preserve the favorable geometry of the original SSL space, we add a cosine-similarity loss that regularizes the adapted token, ensuring the latent space remains smooth and suitable for generation. Our single-token formulation resolves spatial redundancies of 2D latent spaces and significantly reduces training costs. Despite its simplicity and efficiency, RepTok achieves competitive results on class-conditional ImageNet generation and naturally extends to text-to-image synthesis, reaching competitive zero-shot performance on MS-COCO under extremely limited training budgets. Our findings highlight the potential of fine-tuned SSL representations as compact and effective latent spaces for efficient generative modeling.

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

Industrial CAD workflows require robust, generalizable 3D geometric representations supporting accuracy and explainability. We introduce Shape, a self-supervised foundation model converting surface meshes into dense per-token embeddings. Shape combines a structured 3D latent grid, a multi-scale geometry-aware tokenizer (MAGNO) with cross-attention, and a transformer processor using grouped-query attention and RMSNorm. A learned reconstruction prior enables per-region attribution for explainable predictions. Pretraining uses masked-token reconstruction of normalized geometry statistics and multi-resolution contrastive consistency. The 10.9M-parameter backbone is pretrained on 61,052 CAD meshes from Thingi10K, MFCAD, and Fusion360. On a held-out split of 2,983 meshes, Shape achieves reconstruction R2 = 0.729 and 98.1% top-1 retrieval under the Wang-Isola protocol, with near-zero reconstruction train/val gap (contrastive scores use a larger evaluation pool). A 2x2 ablation on loss type and target-space normalization shows per-dimension normalization is critical: without it, performance collapses (R2 < 0.14, top-1 < 88%); with it, both losses succeed (R2 > 0.70, top-1 > 96%). Smooth-L1 offers secondary stability. Code, embeddings, and an interactive demo are released at https://github.com/simd-ai/shape.

Agent systems increasingly use textual skills to encode reusable task procedures, but injecting these skills into the prompt at every step incurs substantial context overhead and exposes skill content as plaintext. We present LatentSkill, a framework that converts textual skills into plug-and-play LoRA adapters through a pretrained hypernetwork. LatentSkill stores skill knowledge in weight space rather than context space, removing per-step skill tokens while preserving modular loading, scaling, and composition. On ALFWorld and Search-QA, LatentSkill outperforms the corresponding in-context skill baseline while using substantially fewer prefill tokens: it improves ALFWorld success by 21.4 and 13.4 points on the seen and unseen splits with 64.1% fewer prefill tokens, and improves Search-QA exact match by 3.0 points with 72.2% lower skill-token overhead. Further analysis shows that generated skill LoRAs form a structured semantic geometry, can be precisely controlled via the LoRA scaling coefficient, and can be composed through parameter-space arithmetic when skill components are aligned. These findings suggest that weight-space skills provide an efficient, modular, and less exposed substrate for extending LLM agents.

Diffusion Language Models (DLMs) have recently emerged as a promising alternative to autoregressive models. Unlike standard diffusion-based approaches, DLMs are not explicitly conditioned on a timestep, raising a natural question: do these models internally represent denoising progress, and how is such information used downstream? In this work, we show that DLMs do in fact encode a latent representation related to the diffusion timestep within their residual streams. We find that this signal can be reliably extracted using probes across layers, indicating that denoising progress is decodable from internal activations. We further demonstrate that steering the model along a low-dimensional subspace associated with the inferred timestep allows us to systematically modulate its notion of denoising progress, leading to predictable changes in model confidence and entropy. Finally, we analyse the geometry of the identified representation, showing that it exhibits structured and interpretable properties in activation space, and shedding light on how such a signal is processed by these models.

Boundary representation (B-Rep) generation is a fundamental task in computer-aided design, yet the direct synthesis of high-fidelity and structurally valid B-Reps remains a major challenge. Existing deep generative methods suffer from two forms of brittleness: representation brittleness, caused by padding noise and feature contamination in the latent space, and generation brittleness, stemming from sequential error propagation and a train-inference mismatch due to non-differentiable validity enforcement. We propose HiFi-BRep, a novel framework that addresses these limitations through two synergistic contributions. First, a topology-aware encoder constructs a high-fidelity latent representation by eliminating padding via learnable queries and preventing feature contamination with topology-guided attention. Second, a single-stage decoder jointly predicts geometry and topology in parallel, embedding core manifold constraints as a differentiable learning objective. This design ensures mutual guidance between geometry and topology while avoiding cascaded errors. Extensive experiments show that HiFi-BRep significantly outperforms state-of-the-art methods in both structural validity and geometric fidelity, providing a robust solution for high-quality B-Rep synthesis. Code and models are publicly available at https://github.com/1nnoh/HiFi-BRep.

We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and point-cloud representations of the input shape and neural operators based on graph and Fourier architectures to learn the solution operator. The graph neural operator handles irregular grids and transforms them into and from regular latent grids on which Fourier neural operator can be efficiently applied. GINO is discretization-convergent, meaning the trained model can be applied to arbitrary discretization of the continuous domain and it converges to the continuum operator as the discretization is refined. To empirically validate the performance of our method on large-scale simulation, we generate the industry-standard aerodynamics dataset of 3D vehicle geometries with Reynolds numbers as high as five million. For this large-scale 3D fluid simulation, numerical methods are expensive to compute surface pressure. We successfully trained GINO to predict the pressure on car surfaces using only five hundred data points. The cost-accuracy experiments show a 26,000 times speed-up compared to optimized GPU-based computational fluid dynamics (CFD) simulators on computing the drag coefficient. When tested on new combinations of geometries and boundary conditions (inlet velocities), GINO obtains a one-fourth reduction in error rate compared to deep neural network approaches.