Geometry-Aware Motion Latents for Learning Robust Manipulation Policies

Learning motion latents for robotic manipulation heavily relies on extracting motion patterns from visual sequences, yet effective action abstractions require understanding three-dimensional geometric transformations. Here, we introduce GeoMoLa (Geometry-Aware Motion Latents), which learns discrete motion latent codes by predicting how point clouds evolve during manipulation rather than reconstructing visual observations. This four-dimensional objective -- spatial geometry changing through time -- forces latent representations to encode actual physical motion rather than appearance patterns. GeoMoLa achieves state-of-the-art performance using only single-view RGB-D input, while existing methods require multi-view reconstruction, succeeding across diverse manipulation benchmarks. Our ablations reveal that geometric prediction is the key to driving performance, quantitatively validating that manipulation depends on spatial understanding. Furthermore, the learned codes exhibit effective motion abstraction: applying them to novel scenes produces physically consistent transformations regardless of visual context. Our real-world experiments also confirm this robustness capability, achieving robust manipulation with minimal demonstrations in cluttered environments where geometric reasoning determines success. Thus, we demonstrate that effective motion latents for robot control can better emerge from understanding motion through its three-dimensional effects rather than pixel-level patterns.

SuperFlex: Deformable Superquadrics for Point Cloud Decomposition

Superquadrics have proven to provide a compact, geometrically meaningful representation for 3D objects. However, existing methods suffer from limited reconstruction accuracy, are restricted to rigid primitives, and lack robustness to partial point clouds. In this work, we present SuperFlex, an enhanced framework that expands the expressive power and applicability of superquadric decompositions. First, we introduce a novel loss formulation which significantly improves reconstruction accuracy. Second, we include bending and tapering deformations, enabling high-fidelity representation of curved and asymmetric geometries. Finally, we leverage these high-quality decompositions as supervision to train a model that is robust to partial real-world point clouds. Experiments demonstrate substantial improvements in reconstruction accuracy over both optimization- and learning-based baselines while maintaining a highly compact primitive representation.

MeshFlow: Mesh Generation with Equivariant Flow Matching

Meshes are among the most common 3D scene representations, but directly generating meshes is challenging because the representation contains important symmetries, including permutation invariance of faces and vertices. MeshFlow learns to generate triangle meshes directly as triangle soups, avoiding the need to serialize meshes into long autoregressive sequences. We adopt equivariant optimal-transport flow matching models that respect the key symmetries of triangle soups: arbitrary permutations of faces and permutations of the vertices within each face. Toward this goal, we propose a simple yet effective modification to the Diffusion Transformer architecture, resulting in a scalable network capable of modeling a velocity field while maintaining the desired equivariance. We further introduce an optimal-transport-based training objective that improves convergence by eliminating supervision signals that violate these symmetries. MeshFlow achieves mesh quality comparable to state-of-the-art autoregressive mesh generators while providing about an 18$\times$ speedup during inference. Project page is at https://qiisun.github.io/MeshFlow/.

Duet: Dual-Robot Understanding via Efficient Teaching

Dual-robot collaboration enables tasks that exceed the reach and payload of a single robot, such as collaboratively transporting objects across environments and executing coordinated handovers. Data acquisition is the primary bottleneck for training these systems. To this end, we introduce DUET, a dual-robot learning framework for mobile manipulation. For efficient data collection, we create a unified dual-embodiment synchronized VR-based teleoperation system for in-domain heterogeneous robot data collection. We further develop a complementary tracking pipeline that records human-human coordination and collaborative mobile manipulation priors. To allow efficient learning, we introduce an Action Chunking Transformer based architecture that first pretrains collaborative policies on efficient human-human demonstrations, before finetuning them on a minimal set of real-robot teleoperation trajectories. We develop a benchmark of four collaborative tasks to evaluate our framework using a Unitree G1 humanoid and a Dexmate Vega1 mobile manipulator. The results demonstrate that harnessing human priors not only yields superior task performance compared to baselines trained only on robot data, but also reduces the total human effort required for data collection. Our human data collection pipeline achieves 5.4x acceleration on average from teleoperation, but we perform equally or better than robot-only data trained policies across all tasks. Our project page is available at https://zhaoy37.github.io/Duet/.

Functional Gradient Descent with Adaptive Representations

Functional optimization problems are typically solved by optimizing the parameters of a fixed representation, such as a neural network, resulting in highly nonconvex losses that complicate both training and theoretical analysis. An interesting alternative is functional gradient descent (FGD), that is, gradient descent directly in function space, which benefits from strong convergence results and admits a clean theory. However, FGD is difficult to implement in practice because functional gradients are infinite-dimensional, and thus cannot be fully computed nor stored in memory. Existing implementations therefore rely on fixed approximations, which introduce approximation error. We propose a new, theoretically-grounded FGD algorithm that adapts the representation of the functional gradients over the course of optimization. By explicitly incorporating this approximation into the analysis, we establish convergence to a stationary point (for smooth losses) and to a global minimizer (under smoothness + a Polyak-Lojasiewicz-type condition) regardless of our approximations. To the best of our knowledge, this is the first implementable FGD method with such guarantees in a general setting. We demonstrate the effectiveness of our method on regression, numerical solution of PDEs, and modern computer vision. Across settings, our method consistently outperforms both FGD with fixed approximations and neural network baselines in efficiency and accuracy.

The Art of Interrogation: Consistency Amplifies Factuality in Spatial Reasoning

Current Large Reasoning Models (LRMs) exhibit remarkable general capabilities but significantly underperform in spatial reasoning tasks. Existing approaches treat this gap as a knowledge deficit, relying on supervised fine-tuning (SFT) to ingest labeled spatial data from external vision sources or synthetic engines. In contrast, we argue that for many tasks, spatial reasoning capabilities are already present in pre-trained LRMs but require alignment through logical coherence under geometric 2D and 3D constraints. In this work, we propose a self-supervised reinforcement learning (RL) framework that targets the internal reasoning process without requiring ground-truth annotations. By formalizing the notion of consistency verifiers -- reward functions that check for geometric and semantic consistency under transformations -- we demonstrate that models can improve their spatial reasoning abilities. We use both image transformations, like flipping, and textual transformations, like swapping the order of objects in the question, and propose a new optimal transport-based RL strategy, OT-GRPO, which is a minimal-matching variant of group relative policy optimization tailored to pairwise verifiers. We show that this label-free consistency training approaches the accuracy of models trained with ground-truth supervision and achieves similar generalization across diverse tasks and data domains.

Planning with the Views via Scene Self-Exploration

Can VLMs predict how each camera move changes the view, and plan many such moves ahead? We call this capability view planning, requiring (1)understanding how a single action transforms the view, and (2)composing many such transformations across multi-turn plans to identify a target view. We probe both abilities in our proposed ViewSuite, a 3D point-cloud environment on real ScanNet scenes. Across 13 frontier VLMs, a critical planning gap emerges: they possess basic view-action knowledge but fail to compose it across multi-turn plans, with the gap widening as viewpoint distance grows. To close this gap, we propose an iterative framework that alternates self-exploration with view graph distillation. The key insight is that all exploration trajectories, regardless of their outcome, collectively form a view graph that compactly captures how viewpoints connect across a scene. Distilling this graph into diverse supervised tasks reshapes the policy distribution and overcomes the sparse rewards that stall pure RL. This improves Qwen2.5-VL-7B from 2.5% to 47.8% on interactive view planning, surpassing GPT-5.4 Pro (18.5%) and Gemini 3.1 Pro (21.4%). Self-exploration emerges as a promising path toward VLMs that can actively reason and plan in 3D space.

Fishbone: From One 3D Asset to a Million Controllable Edits

Large-scale controllable 3D assets are critical for computer graphics, embodied AI, robotics, and interactive content creation, yet creating diverse 3D assets remains challenging due to the high cost of manual modeling and rigging. Shape deformation offers a natural way to generate variations from existing meshes, but existing data-driven methods often rely on sparse user inputs, while parametric editing frameworks require manually designed control structures and category-specific configurations. Inspired by natural creatures, where a central spine governs global shape and cross-sectional ribs control local variation, we introduce Fishbone, a unified rib-spine representation for general shapes that supports controllable parametric mesh deformation, reduced-space dynamics, and animation. Given an input mesh, Fishbone computes a geodesic scalar field with an adaptive heat method, extracts iso-contours as cross-sectional ribs, constructs a smooth geometry-aware spine through rib centers, and associates surface vertices with nearby rib and spine structures using Gaussian-weighted skinning. The resulting representation enables real-time and predictable deformation: ribs control local profiles such as thickness, orientation, and cross-sectional variation, while the spine controls global bending, twisting, and stretching. The same structure also supports reduced-space simulation and keyframe animation. We further construct Fishbone-136K by augmenting Hunyuan3D with rib-spine structures, and demonstrate applications in controllable 3D generation, deformation-based data augmentation for robot learning, interactive mesh editing, and agentic generation. Experiments demonstrate the effectiveness, efficiency, and versatility of the proposed framework.

ESI-Bench: Towards Embodied Spatial Intelligence that Closes the Perception-Action Loop

Spatial intelligence unfolds through a perception-action loop: agents act to acquire observations, and reason about how observations vary as a function of action. Rather than passively processing what is seen, they actively uncover what is unseen - occluded structure, dynamics, containment, and functionality that cannot be resolved from passive sensing alone. We move beyond prior formulations of spatial intelligence that assume oracle observations by recasting the observer as an actor. We introduce ESI-BENCH, a comprehensive benchmark for embodied spatial intelligence spanning 10 task categories and 29 subcategories built on OmniGibson, grounded in Spelke's core knowledge systems. Agents must decide what abilities to deploy - perception, locomotion, and manipulation - and how to sequence them to actively accumulate task-relevant evidence. We conduct extensive experiments on state-of-the-art MLLMs and find that active exploration substantially outperforms passive counterparts, with agents spontaneously discovering emergent spatial strategies without explicit instructions, while random multi-view often adds noise rather than signal despite consuming far more images. Most failures stem not from weak perception but from action blindness: poor action choices lead to poor observations, which in turn drive cascading errors. While explicit 3D grounding stabilizes reasoning on depth-sensitive tasks, imperfect 3D representation proves more harmful than 2D baselines by distorting spatial relations. Human studies further reveal that unlike humans who seek falsifying viewpoints and revise beliefs under contradiction, models commit prematurely with high confidence regardless of evidence quality, exposing a metacognitive gap that neither better perception nor more embodied interaction alone can close.

OCH3R: Object-Centric Holistic 3D Reconstruction

Object-centric scene understanding is a fundamental challenge in computer vision. Existing approaches often rely on multi-stage pipelines that first apply pre-trained segmentors to extract individual objects, followed by per-object 3D reconstruction. Such methods are computationally expensive, fragile to segmentation errors, and scale poorly with scene complexity. We introduce OCH3R, a unified framework for Object-Centric Holistic 3D Reconstruction from a single RGB image. OCH3R performs one forward pass to simultaneously predict all object instances with their 6D poses and detailed 3D reconstructions. The key idea is a transformer architecture that predicts per-pixel attributes, including CLIP-based category embeddings, metric depth, normalized object coordinates (NOCS), and a fixed number of 3D Gaussians representing each object. To supervise these Gaussian reconstructions, we transform them into canonical space using the predicted 6D poses and align them with pre-rendered canonical ground truth, avoiding costly per-image Gaussian label generation. On standard indoor benchmarks, OCH3R achieves state-of-the-art performance across monocular depth estimation, open-vocabulary semantic segmentation, and RGB-only category-level 6D pose estimation, while producing high-fidelity, editable per-object reconstructions. Crucially, inference is fully feed-forward and scales independently of the number of objects, offering orders-of-magnitude speedups over conventional multi-stage pipelines in cluttered scenes.