We present Orbit-Space Geometric Probability Paths (OGPP) , a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries , so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; (ii) particles live in physical space, so the flow's terminal velocity has physical meaning and can encode geometric attributes (e.g., surface normals). OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state-of-the-art with 5× fewer steps and reaches airplane EMD comparable to DiT-3D with 26× fewer parameters and 5× fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

We present MoGe, a powerful model for recovering 3D geometry from monocular open-domain images. Given a single image, our model directly predicts a 3D point map of the captured scene with an affine-invariant representation, which is agnostic to true global scale and shift. This new representation precludes ambiguous supervision in training and facilitates effective geometry learning. Furthermore, we propose a set of novel global and local geometry supervision techniques that empower the model to learn high-quality geometry. These include a robust, optimal, and efficient point cloud alignment solver for accurate global shape learning, and a multi-scale local geometry loss promoting precise local geometry supervision. We train our model on a large, mixed dataset and demonstrate its strong generalizability and high accuracy. In our comprehensive evaluation on diverse unseen datasets, our model significantly outperforms state-of-the-art methods across all tasks, including monocular estimation of 3D point map, depth map, and camera field of view.

We introduce a novel 3D generation method for versatile and high-quality 3D asset creation. The cornerstone is a unified Structured LATent (SLat) representation which allows decoding to different output formats, such as Radiance Fields, 3D Gaussians, and meshes. This is achieved by integrating a sparsely-populated 3D grid with dense multiview visual features extracted from a powerful vision foundation model, comprehensively capturing both structural (geometry) and textural (appearance) information while maintaining flexibility during decoding.We employ rectified flow transformers tailored for SLat as our 3D generation models and train models with up to 2 billion parameters on a large 3D asset dataset of 500K diverse objects. Our model generates high-quality results with text or image conditions, significantly surpassing existing methods, including recent ones at similar scales. We showcase flexible output format selection and local 3D editing capabilities which were not offered by previous models. Project Page: trellis3d.github.io.

We propose MoGe-2, an advanced open-domain geometry estimation model that recovers a metric-scale 3D point map of a scene from a single image. Our method builds upon the recent monocular geometry estimation approach, MoGe, which predicts affine-invariant point maps with unknown scales. We explore effective strategies to extend MoGe for metric geometry prediction without compromising the relative geometry accuracy provided by the affine-invariant point representation. Additionally, we discover that noise and errors in real data diminish fine-grained detail in the predicted geometry. We address this by developing a data refinement approach that filters and completes real data using sharp synthetic labels, significantly enhancing the granularity of the reconstructed geometry while maintaining the overall accuracy. We train our model on a large corpus of mixed datasets and conducted comprehensive evaluations, demonstrating its superior performance in achieving accurate relative geometry, precise metric scale, and fine-grained detail recovery -- capabilities that no previous methods have simultaneously achieved.

We propose the Epsilon Difference Gradient Evolution (EDGE) method for accurate flow-map calculation on grids via Hermite interpolation without using velocity buffers. Our key idea is to integrate Gradient Evolution for accurate first-order derivatives and a tetrahedron-based Epsilon Difference scheme to compute higher-order derivatives with reduced memory consumption. EDGE achieves O (1) memory usage, independent of flow map length, while maintaining vorticity preservation comparable to buffer-based methods. We validate our methods across diverse vortical flow scenarios, demonstrating up to 90% backward map memory reduction and significant computational efficiency, broadening the applicability of flow-map methods to large-scale and complex fluid simulations.

We propose Leapfrog Flow Maps (LFM) to simulate incompressible fluids with rich vortical flows in real time. Our key idea is to use a hybrid velocityimpulse scheme enhanced with leapfrog method to reduce the computational workload of impulse-based flow map methods, while possessing strong ability to preserve vortical structures and fluid details. In order to accelerate the impulse-to-velocity projection, we develop a fast matrix-free Algebraic Multigrid Preconditioned Conjugate Gradient (AMGPCG) solver with customized GPU optimization, which makes projection comparable with impulse evolution in terms of time cost. We demonstrate the performance of our method and its efficacy in a wide range of examples and experiments, such as real-time simulated burning fire ball and delta wingtip vortices.

This paper introduces a novel Induce-on-Boundary (IoB) solver designed to address the magnetostatic governing equations of ferrofluids. The IoB solver is based on a single-layer potential and utilizes only the surface point cloud of the object, offering a lightweight, fast, and accurate solution for calculating magnetic fields. Compared to existing methods, it eliminates the need for complex linear system solvers and maintains minimal computational complexities. Moreover, it can be seamlessly integrated into conventional fluid simulators without compromising boundary conditions. Through extensive theoretical analysis and experiments, we validate both the convergence and scalability of the IoB solver, achieving state-of-the-art performance. Additionally, a straightforward coupling approach is proposed and executed to showcase the solver's effectiveness when integrated into a grid-based fluid simulation pipeline, allowing for realistic simulations of representative ferrofluid instabilities.

In this work, we tackle the problem of learning universal robotic dexterous grasping from a point cloud observation under a table-top setting. The goal is to grasp and lift up objects in high-quality and diverse ways and generalize across hundreds of categories and even the unseen. Inspired by successful pipelines used in parallel gripper grasping, we split the task into two stages: 1) grasp proposal (pose) generation and 2) goal-conditioned grasp execution. For the first stage, we propose a novel probabilistic model of grasp pose conditioned on the point cloud observation that factorizes rotation from translation and articulation. Trained on our synthesized large-scale dexterous grasp dataset, this model enables us to sample diverse and high-quality dexterous grasp poses for the object point cloud. For the second stage, we propose to replace the motion planning used in parallel gripper grasping with a goal-conditioned grasp policy, due to the complexity involved in dexterous grasping execution. Note that it is very challenging to learn this highly generalizable grasp policy that only takes realistic inputs without oracle states. We thus propose several important innovations, including state canonicalization, object curriculum, and teacher-student distillation. In-tegrating the two stages, our final pipeline becomes the first to achieve universal generalization for dexterous grasping, demonstrating an average success rate of more than 60% on thousands of object instances, which significantly out-performs all baselines, meanwhile showing only a minimal generalization gap.

Robotic dexterous grasping is the first step to enable human-like dexterous object manipulation and thus a crucial robotic technology. However, dexterous grasping is much more under-explored than object grasping with parallel grippers, partially due to the lack of a large-scale dataset. In this work, we present a large-scale robotic dexterous grasp dataset, DexGraspNet, generated by our proposed highly efficient synthesis method that can be generally applied to any dexterous hand. Our method leverages a deeply accelerated differentiable force closure estimator and thus can efficiently and robustly synthesize stable and diverse grasps on a large scale. We choose ShadowHand and generate 1.32 million grasps for 5355 objects, covering more than 133 object categories and containing more than 200 diverse grasps for each object instance, with all grasps having been validated by the Isaac Gym simulator. Compared to the previous dataset from Liu et al. generated by GraspIt!, our dataset has not only more objects and grasps, but also higher diversity and quality. Via performing cross-dataset experiments, we show that training several algorithms of dexterous grasp synthesis on our dataset significantly outperforms training on the previous one. To access our data and code, including code for human and Allegro grasp synthesis, please visit our project page: https://pku-epic.github.io/DexGraspNet/.

The VirtualCube system is a 3D video conference system that attempts to overcome some limitations of conventional technologies. The key ingredient is VirtualCube, an abstract representation of a real-world cubicle instrumented with RGBD cameras for capturing the user's 3D geometry and texture. We design VirtualCube so that the task of data capturing is standardized and significantly simplified, and everything can be built using off-the-shelf hardware. We use VirtualCubes as the basic building blocks of a virtual conferencing environment, and we provide each VirtualCube user with a surrounding display showing life-size videos of remote participants. To achieve real-time rendering of remote participants, we develop the V-Cube View algorithm, which uses multi-view stereo for more accurate depth estimation and Lumi-Net rendering for better rendering quality. The VirtualCube system correctly preserves the mutual eye gaze between participants, allowing them to establish eye contact and be aware of who is visually paying attention to them. The system also allows a participant to have side discussions with remote participants as if they were in the same room. Finally, the system sheds lights on how to support the shared space of work items (e.g., documents and applications) and track participants' visual attention to work items.