Molecular Representations in Implicit Functional Space via Hyper-Networks

Molecular representations fundamentally shape how machine learning systems reason about molecular structure and physical properties. Most existing approaches adopt a discrete pipeline: molecules are encoded as sequences, graphs, or point clouds, mapped to fixed-dimensional embeddings, and then used for task-specific prediction. This paradigm treats molecules as discrete objects, despite their intrinsically continuous and field-like physical nature. We argue that molecular learning can instead be formulated as learning in function space. Specifically, we model each molecule as a continuous function over three-dimensional (3D) space and treat this molecular field as the primary object of representation. From this perspective, conventional molecular representations arise as particular sampling schemes of an underlying continuous object. We instantiate this formulation with MolField, a hyper-network-based framework that learns distributions over molecular fields. To ensure physical consistency, these functions are defined over canonicalized coordinates, yielding invariance to global SE(3) transformations. To enable learning directly over functions, we introduce a structured weight tokenization and train a sequence-based hyper-network to model a shared prior over molecular fields. We evaluate MolField on molecular dynamics and property prediction. Our results show that treating molecules as continuous functions fundamentally changes how molecular representations generalize across tasks and yields downstream behavior that is stable to how molecules are discretized or queried.

Proc3D: Procedural 3D Generation and Parametric Editing of 3D Shapes with Large Language Models

Generating 3D models has traditionally been a complex task requiring specialized expertise. While recent advances in generative AI have sought to automate this process, existing methods produce non-editable representation, such as meshes or point clouds, limiting their adaptability for iterative design. In this paper, we introduce Proc3D, a system designed to generate editable 3D models while enabling real-time modifications. At its core, Proc3D introduces procedural compact graph (PCG), a graph representation of 3D models, that encodes the algorithmic rules and structures necessary for generating the model. This representation exposes key parameters, allowing intuitive manual adjustments via sliders and checkboxes, as well as real-time, automated modifications through natural language prompts using Large Language Models (LLMs). We demonstrate Proc3D's capabilities using two generative approaches: GPT-4o with in-context learning (ICL) and a fine-tuned LLAMA-3 model. Experimental results show that Proc3D outperforms existing methods in editing efficiency, achieving more than 400x speedup over conventional approaches that require full regeneration for each modification. Additionally, Proc3D improves ULIP scores by 28%, a metric that evaluates the alignment between generated 3D models and text prompts. By enabling text-aligned 3D model generation along with precise, real-time parametric edits, Proc3D facilitates highly accurate text-based image editing applications.

Joint Semantic and Rendering Enhancements in 3D Gaussian Modeling with Anisotropic Local Encoding

Recent works propose extending 3DGS with semantic feature vectors for simultaneous semantic segmentation and image rendering. However, these methods often treat the semantic and rendering branches separately, relying solely on 2D supervision while ignoring the 3D Gaussian geometry. Moreover, current adaptive strategies adapt the Gaussian set depending solely on rendering gradients, which can be insufficient in subtle or textureless regions. In this work, we propose a joint enhancement framework for 3D semantic Gaussian modeling that synergizes both semantic and rendering branches. Firstly, unlike conventional point cloud shape encoding, we introduce an anisotropic 3D Gaussian Chebyshev descriptor using the Laplace-Beltrami operator to capture fine-grained 3D shape details, thereby distinguishing objects with similar appearances and reducing reliance on potentially noisy 2D guidance. In addition, without relying solely on rendering gradient, we adaptively adjust Gaussian allocation and spherical harmonics with local semantic and shape signals, enhancing rendering efficiency through selective resource allocation. Finally, we employ a cross-scene knowledge transfer module to continuously update learned shape patterns, enabling faster convergence and robust representations without relearning shape information from scratch for each new scene. Experiments on multiple datasets demonstrate improvements in segmentation accuracy and rendering quality while maintaining high rendering frame rates.

Enhanced 3D Shape Analysis via Information Geometry

Three-dimensional point clouds provide highly accurate digital representations of objects, essential for applications in computer graphics, photogrammetry, computer vision, and robotics. However, comparing point clouds faces significant challenges due to their unstructured nature and the complex geometry of the surfaces they represent. Traditional geometric metrics such as Hausdorff and Chamfer distances often fail to capture global statistical structure and exhibit sensitivity to outliers, while existing Kullback-Leibler (KL) divergence approximations for Gaussian Mixture Models can produce unbounded or numerically unstable values. This paper introduces an information geometric framework for 3D point cloud shape analysis by representing point clouds as Gaussian Mixture Models (GMMs) on a statistical manifold. We prove that the space of GMMs forms a statistical manifold and propose the Modified Symmetric Kullback-Leibler (MSKL) divergence with theoretically guaranteed upper and lower bounds, ensuring numerical stability for all GMM comparisons. Through comprehensive experiments on human pose discrimination (MPI-FAUST dataset) and animal shape comparison (G-PCD dataset), we demonstrate that MSKL provides stable and monotonically varying values that directly reflect geometric variation, outperforming traditional distances and existing KL approximations.

Repurposing 2D Diffusion Models for 3D Shape Completion

We present a framework that adapts 2D diffusion models for 3D shape completion from incomplete point clouds. While text-to-image diffusion models have achieved remarkable success with abundant 2D data, 3D diffusion models lag due to the scarcity of high-quality 3D datasets and a persistent modality gap between 3D inputs and 2D latent spaces. To overcome these limitations, we introduce the Shape Atlas, a compact 2D representation of 3D geometry that (1) enables full utilization of the generative power of pretrained 2D diffusion models, and (2) aligns the modalities between the conditional input and output spaces, allowing more effective conditioning. This unified 2D formulation facilitates learning from limited 3D data and produces high-quality, detail-preserving shape completions. We validate the effectiveness of our results on the PCN and ShapeNet-55 datasets. Additionally, we show the downstream application of creating artist-created meshes from our completed point clouds, further demonstrating the practicality of our method.

LoG3D: Ultra-High-Resolution 3D Shape Modeling via Local-to-Global Partitioning

Generating high-fidelity 3D contents remains a fundamental challenge due to the complexity of representing arbitrary topologies-such as open surfaces and intricate internal structures-while preserving geometric details. Prevailing methods based on signed distance fields (SDFs) are hampered by costly watertight preprocessing and struggle with non-manifold geometries, while point-cloud representations often suffer from sampling artifacts and surface discontinuities. To overcome these limitations, we propose a novel 3D variational autoencoder (VAE) framework built upon unsigned distance fields (UDFs)-a more robust and computationally efficient representation that naturally handles complex and incomplete shapes. Our core innovation is a local-to-global (LoG) architecture that processes the UDF by partitioning it into uniform subvolumes, termed UBlocks. This architecture couples 3D convolutions for capturing local detail with sparse transformers for enforcing global coherence. A Pad-Average strategy further ensures smooth transitions at subvolume boundaries during reconstruction. This modular design enables seamless scaling to ultra-high resolutions up to $2048^3$-a regime previously unattainable for 3D VAEs. Experiments demonstrate state-of-the-art performance in both reconstruction accuracy and generative quality, yielding superior surface smoothness and geometric flexibility.

FUSE: A Flow-based Mapping Between Shapes

We introduce a novel neural representation for maps between 3D shapes based on flow-matching models, which is computationally efficient and supports cross-representation shape matching without large-scale training or data-driven procedures. 3D shapes are represented as the probability distribution induced by a continuous and invertible flow mapping from a fixed anchor distribution. Given a source and a target shape, the composition of the inverse flow (source to anchor) with the forward flow (anchor to target), we continuously map points between the two surfaces. By encoding the shapes with a pointwise task-tailored embedding, this construction provides an invertible and modality-agnostic representation of maps between shapes across point clouds, meshes, signed distance fields (SDFs), and volumetric data. The resulting representation consistently achieves high coverage and accuracy across diverse benchmarks and challenging settings in shape matching. Beyond shape matching, our framework shows promising results in other tasks, including UV mapping and registration of raw point cloud scans of human bodies.

Voronoi-Assisted Diffusion for Computing Unsigned Distance Fields from Unoriented Points

Unsigned Distance Fields (UDFs) provide a flexible representation for 3D shapes with arbitrary topology, including open and closed surfaces, orientable and non-orientable geometries, and non-manifold structures. While recent neural approaches have shown promise in learning UDFs, they often suffer from numerical instability, high computational cost, and limited controllability. We present a lightweight, network-free method, Voronoi-Assisted Diffusion (VAD), for computing UDFs directly from unoriented point clouds. Our approach begins by assigning bi-directional normals to input points, guided by two Voronoi-based geometric criteria encoded in an energy function for optimal alignment. The aligned normals are then diffused to form an approximate UDF gradient field, which is subsequently integrated to recover the final UDF. Experiments demonstrate that VAD robustly handles watertight and open surfaces, as well as complex non-manifold and non-orientable geometries, while remaining computationally efficient and stable.

MeshCoder: LLM-Powered Structured Mesh Code Generation from Point Clouds

Reconstructing 3D objects into editable programs is pivotal for applications like reverse engineering and shape editing. However, existing methods often rely on limited domain-specific languages (DSLs) and small-scale datasets, restricting their ability to model complex geometries and structures. To address these challenges, we introduce MeshCoder, a novel framework that reconstructs complex 3D objects from point clouds into editable Blender Python scripts. We develop a comprehensive set of expressive Blender Python APIs capable of synthesizing intricate geometries. Leveraging these APIs, we construct a large-scale paired object-code dataset, where the code for each object is decomposed into distinct semantic parts. Subsequently, we train a multimodal large language model (LLM) that translates 3D point cloud into executable Blender Python scripts. Our approach not only achieves superior performance in shape-to-code reconstruction tasks but also facilitates intuitive geometric and topological editing through convenient code modifications. Furthermore, our code-based representation enhances the reasoning capabilities of LLMs in 3D shape understanding tasks. Together, these contributions establish MeshCoder as a powerful and flexible solution for programmatic 3D shape reconstruction and understanding.

Point cloud segmentation for 3D Clothed Human Layering

3D Cloth modeling and simulation is essential for avatars creation in several fields, such as fashion, entertainment, and animation. Achieving high-quality results is challenging due to the large variability of clothed body especially in the generation of realistic wrinkles. 3D scan acquisitions provide more accuracy in the representation of real-world objects but lack semantic information that can be inferred with a reliable semantic reconstruction pipeline. To this aim, shape segmentation plays a crucial role in identifying the semantic shape parts. However, current 3D shape segmentation methods are designed for scene understanding and interpretation and only few work is devoted to modeling. In the context of clothed body modeling the segmentation is a preliminary step for fully semantic shape parts reconstruction namely the underlying body and the involved garments. These parts represent several layers with strong overlap in contrast with standard segmentation methods that provide disjoint sets. In this work we propose a new 3D point cloud segmentation paradigm where each 3D point can be simultaneously associated to different layers. In this fashion we can estimate the underlying body parts and the unseen clothed regions, i.e., the part of a cloth occluded by the clothed-layer above. We name this segmentation paradigm clothed human layering. We create a new synthetic dataset that simulates very realistic 3D scans with the ground truth of the involved clothing layers. We propose and evaluate different neural network settings to deal with 3D clothing layering. We considered both coarse and fine grained per-layer garment identification. Our experiments demonstrates the benefit in introducing proper strategies for the segmentation on the garment domain on both the synthetic and real-world scan datasets.