We introduce Motion2VecSets, a 4D diffusion model for dynamic surface mesh generation from various ambiguous observations, including a sequence of RGB images, sparse and partial point clouds, and low-resolution voxel grids. While recent methods using neural field representations have shown success in modeling non-rigid objects, conventional feed-forward architectures struggle with noisy, partial, or sparse observations due to their deterministic nature. To address the inherent one-to-many mapping problem, we introduce a diffusion model that explicitly learns the shape and motion distribution of non-rigid objects through an iterative denoising process of compressed latent representations. The diffusion-based priors provide more plausible and diverse reconstructions under ambiguous conditions. Instead of relying on global latent codes, we represent 4D dynamics using latent sets. This novel 4D representation captures local shape and deformation patterns, leading to more accurate non-linear motion capture and significantly improving generalization capacity to unseen motions and identities. For temporally coherent tracking, we jointly denoise latent sets across frames and enable cross-frame information exchange. To reduce computational cost, we design an interleaved spatial-temporal attention block that alternately aggregates deformation latents along spatial and temporal dimensions. Extensive experiments on datasets of humans, animals, and articulated objects demonstrate that Motion2VecSets outperforms prior methods in reconstructing and tracking non-rigid deformations from various imperfect observations.

Generating high-quality triangle meshes is essential for film, gaming, and interactive 3D applications. Mainstream methods rely on mesh serialization and autoregressive processes, which stuggles in effective inference and is sensitive to error accumulation. In this paper, we present Nexus , a diffusion method that achieves holistic mesh generation via decoupled vertex and topology generation. First, we view mesh vertices as sparse voxels organized as an octree and adopt a diffusion model to generate the vertices in a coarse-to-fine manner. Second, for topology modeling, we propose Space-time Interval , as an extension of Spacetime Distance to encode arbitrary edge and face topology into continuous per-vertex embeddings. It allows for a global and efficient recovery of complex topology. We then employ a diffusion model to generate the continuous embeddings on the generated vertices. Extensive experiments on the Objaverse and Toys4K datasets and in-the-wild images demonstrate that our method outperforms state-of-the-art autoregressive and two-stage baselines, effectively circumventing the inherent limitations of sequential mesh modeling. A blind user study from 3D practitioners confirms strong perceptual preference for our results.

We present V2M4, a novel 4D reconstruction method that directly generates a usable 4D mesh animation asset from a single monocular video. Unlike existing approaches that rely on priors from multi-view image and video generation models, our method is based on native 3D mesh generation models. Naively applying 3D mesh generation models to generate a mesh for each frame in a 4D task can lead to issues such as incorrect mesh poses, misalignment of mesh appearance, and inconsistencies in mesh geometry and texture maps. To address these problems, we propose a structured workflow that includes camera search and mesh reposing, condition embedding optimization for mesh appearance refinement, pairwise mesh registration for topology consistency, and global texture map optimization for texture consistency. Our method outputs high-quality 4D animated assets that are compatible with mainstream graphics and game software. Experimental results across a variety of animation types and motion amplitudes demonstrate the generalization and effectiveness of our method. Project page: https://windvchen.github.io/V2M4/.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

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.

We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to convolutional networks, we introduce longer-range skip connections to complement this multi-resolution approach. The key advantages of this architecture are the faster processing speed and lower memory consumption. We are, therefore, able to process more complex trees than would be possible with a vanilla transformer architecture. Furthermore, we extend this approach to perform image-to-tree and point-cloud-to-tree conditional generation and to simulate the tree growth processes, generating 4D trees. Empirical results validate our approach in terms of speed, memory consumption, and generation quality.

Boundary representation (B-rep) is the de facto standard for CAD model representation in modern industrial design. The intricate coupling between geometric and topological elements in B-rep structures has forced existing generative methods to rely on cascaded multi-stage networks, resulting in error accumulation and computational inefficiency. We present BrepGPT, a single-stage autoregressive framework for B-rep generation. Our key innovation lies in the Voronoi Half-Patch (VHP) representation, which decomposes B-reps into unified local units by assigning geometry to nearest half-edges and sampling their next pointers. Unlike hierarchical representations that require multiple distinct encodings for different structural levels, our VHP representation facilitates unifying geometric attributes and topological relations in a single, coherent format. We further leverage dual VQ-VAEs to encode both vertex topology and Voronoi Half-Patches into vertex-based tokens, achieving a more compact sequential encoding. A decoder-only Transformer is then trained to autoregressively predict these tokens, which are subsequently mapped to vertex-based features and decoded into complete B-rep models. Experiments demonstrate that BrepGPT achieves state-of-the-art performance in unconditional B-rep generation. The framework also exhibits versatility in various applications, including conditional generation from category labels, point clouds, text descriptions, and images, as well as B-rep autocompletion and interpolation.

We propose functional diffusion, a generative diffusion model focused on infinite-dimensional function data samples. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be seen as an extension of classical diffusion models to an infinite-dimensional domain. Functional diffusion is very versatile as images, videos, audio, 3D shapes, deformations, etc., can be handled by the same framework with minimal changes. In addition, functional diffusion is especially suited for irregular data or data defined in non-standard domains. In our work, we derive the necessary foundations for functional diffusion and propose a first implementation based on the transformer architecture. We show generative results on complicated signed distance functions and deformation functions defined on 3D surfaces.

We introduce Motion2VecSets, a 4D diffusion model for dynamic surface reconstruction from point cloud sequences. While existing state-of-the-art methods have demonstrated success in reconstructing non-rigid objects using neural field representations, conventional feed-forward networks encounter challenges with ambiguous observations from noisy, partial, or sparse point clouds. To address these challenges, we introduce a diffusion model that explicitly learns the shape and motion distribution of non-rigid objects through an iterative denoising process of compressed latent representations. The diffusion-based priors enable more plausible and probabilistic reconstructions when handling ambiguous inputs. We parameterize 4D dynamics with latent sets instead of using global latent codes. This novel 4D representation allows us to learn local shape and deformation patterns, leading to more accurate nonlinear motion capture and significantly improving generalizability to unseen motions and identities. For more temporally-coherent object tracking, we synchronously denoise deformation latent sets and exchange information across multiple frames. To avoid computational overhead, we designed an interleaved space and time attention block to alternately aggregate deformation latents along spatial and temporal domains. Extensive comparisons against state-of-the-art methods demonstrate the superiority of our Motion2VecSets in 4D reconstruction from various imperfect observations.

While diffusion models have shown impressive performance in 2D image/video generation, diffusion-based Text-to-Multi-view-Video (T2MVid) generation remains underexplored. The new challenges posed by T2MVid generation lie in the lack of massive captioned multi-view videos and the complexity of modeling such multi-dimensional distribution. To this end, we propose a novel diffusion-based pipeline that generates high-quality multi-view videos centered around a dynamic 3D object from text. Specifically, we factor the T2MVid problem into viewpoint-space and time components. Such factorization allows us to combine and reuse layers of advanced pre-trained multi-view image and 2D video diffusion models to ensure multi-view consistency as well as temporal coherence for the generated multi-view videos, largely reducing the training cost. We further introduce alignment modules to align the latent spaces of layers from the pre-trained multi-view and the 2D video diffusion models, addressing the reused layers' incompatibility that arises from the domain gap between 2D and multi-view data. In support of this and future research, we further contribute a captioned multi-view video dataset. Experimental results demonstrate that our method generates high-quality multi-view videos, exhibiting vivid motions, temporal coherence, and multi-view consistency, given a variety of text prompts.

We introduce 3DShape2VecSet, a novel shape representation for neural fields designed for generative diffusion models. Our shape representation can encode 3D shapes given as surface models or point clouds, and represents them as neural fields. The concept of neural fields has previously been combined with a global latent vector, a regular grid of latent vectors, or an irregular grid of latent vectors. Our new representation encodes neural fields on top of a set of vectors. We draw from multiple concepts, such as the radial basis function representation, and the cross attention and self-attention function, to design a learnable representation that is especially suitable for processing with transformers. Our results show improved performance in 3D shape encoding and 3D shape generative modeling tasks. We demonstrate a wide variety of generative applications: unconditioned generation, category-conditioned generation, text-conditioned generation, point-cloud completion, and image-conditioned generation. Code: https://1zb.github.io/3DShape2VecSet/.

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 being defined on a regular grid. In contrast, we define latents on irregular grids which facilitates 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 of 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.

In this paper we propose a new framework for point cloud instance segmentation. Our framework has two steps: an embedding step and a clustering step. In the embedding step, our main contribution is to propose a probabilistic embedding space for point cloud embedding. Specifically, each point is represented as a tri-variate normal distribution. In the clustering step, we propose a novel loss function, which benefits both the semantic segmentation and the clustering. Our experimental results show important improvements to the SOTA, i.e., 3.1% increased average per-category mAP on the PartNet dataset.

We propose a novel and flexible roof modeling approach that can be used for constructing planar 3D polygon roof meshes. Our method uses a graph structure to encode roof topology and enforces the roof validity by optimizing a simple but effective planarity metric we propose. This approach is significantly more efficient than using general purpose 3D modeling tools such as 3ds Max or SketchUp, and more powerful and expressive than specialized tools such as the straight skeleton. Our optimization-based formulation is also flexible and can accommodate different styles and user preferences for roof modeling. We showcase two applications. The first application is an interactive roof editing framework that can be used for roof design or roof reconstruction from aerial images. We highlight the efficiency and generality of our approach by constructing a mesh-image paired dataset consisting of 2539 roofs. Our second application is a generative model to synthesize new roof meshes from scratch. We use our novel dataset to combine machine learning and our roof optimization techniques, by using transformers and graph convolutional networks to model roof topology, and our roof optimization methods to enforce the planarity constraint.

As compared to the conventional RGB or gray-scale images, multispectral images (MSI) can deliver more faithful representation for real scenes, and enhance the performance of many computer vision tasks. In practice, however, an MSI is always corrupted by various noises. In this paper we propose an effective MSI denoising approach by combinatorially considering two intrinsic characteristics underlying an MSI: the nonlocal similarity over space and the global correlation across spectrum. In specific, by explicitly considering spatial self-similarity of an MSI we construct a nonlocal tensor dictionary learning model with a group-block-sparsity constraint, which makes similar full-band patches (FBP) share the same atoms from the spatial and spectral dictionaries. Furthermore, through exploiting spectral correlation of an MSI and assuming over-redundancy of dictionaries, the constrained nonlocal MSI dictionary learning model can be decomposed into a series of unconstrained low-rank tensor approximation problems, which can be readily solved by off-the-shelf higher order statistics. Experimental results show that our method outperforms all state-of-the-art MSI denoising methods under comprehensive quantitative performance measures.