# DualBrep: A Dual-Field Continuous Representation for B-rep Modelling arXiv: https://arxiv.org/abs/2606.31579 ยท HTML: https://mlsanity.com/paper/2606.31579/ ## Key facts - Cited by 2 papers in the map (data through 14 Oct 2026). - Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models. - Builds on 26 of its 44 references that are in the map. - First posted on arXiv 30 Jun 2026. ## Placed in - Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/) ## Builds on (most cited first, 26 of 26) - [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023) - [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019) - [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018) - [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024) - [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016) - [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023) - [Hunyuan3D 2.0: Scaling Diffusion Models for High Resolution Textured 3D Assets Generation](https://mlsanity.com/paper/2501.12202/) (2025) - [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018) - [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021) - [XCube: Large-Scale 3D Generative Modeling using Sparse Voxel Hierarchies](https://mlsanity.com/paper/2312.03806/) (2023) - [SkexGen: Autoregressive Generation of CAD Construction Sequences with Disentangled Codebooks](https://mlsanity.com/paper/2207.04632/) (2022) - [BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry](https://mlsanity.com/paper/2401.15563/) (2024) - [ParSeNet: A Parametric Surface Fitting Network for 3D Point Clouds](https://mlsanity.com/paper/2003.12181/) (2020) - [BRepNet: A topological message passing system for solid models](https://mlsanity.com/paper/2104.00706/) (2021) - [Sparc3D: Sparse Representation and Construction for High-Resolution 3D Shapes Modeling](https://mlsanity.com/paper/2505.14521/) (2025) - [Hierarchical Neural Coding for Controllable CAD Model Generation](https://mlsanity.com/paper/2307.00149/) (2023) - [Fusion 360 Gallery: A Dataset and Environment for Programmatic CAD Construction from Human Design Sequences](https://mlsanity.com/paper/2010.02392/) (2020) - [HPNet: Deep Primitive Segmentation Using Hybrid Representations](https://mlsanity.com/paper/2105.10620/) (2021) - [HoLa: B-Rep Generation using a Holistic Latent Representation](https://mlsanity.com/paper/2504.14257/) (2025) - [DTGBrepGen: A Novel B-rep Generative Model through Decoupling Topology and Geometry](https://mlsanity.com/paper/2503.13110/) (2025) - [NeuralVDB: High-resolution Sparse Volume Representation using Hierarchical Neural Networks](https://mlsanity.com/paper/2208.04448/) (2022) - [Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning](https://mlsanity.com/paper/2406.05261/) (2024) - [ComplexGen: CAD Reconstruction by B-Rep Chain Complex Generation](https://mlsanity.com/paper/2205.14573/) (2022) - [AutoBrep: Autoregressive B-Rep Generation with Unified Topology and Geometry](https://mlsanity.com/paper/2512.03018/) (2025) - [BrepGPT: Autoregressive B-rep Generation with Voronoi Half-Patch](https://mlsanity.com/paper/2511.22171/) (2025) - [Aligning Constraint Generation with Design Intent in Parametric CAD](https://mlsanity.com/paper/2504.13178/) (2025) ## Built on by (most cited first, 2 of 2) - [CADENA: Stepwise CAD Reverse Engineering](https://mlsanity.com/paper/2608.00799/) (2026) - [Learn the Solid, Not the File: Canonical Inputs for Neural Networks on CAD Boundary Representations](https://mlsanity.com/paper/2609.11573/) (2026) ## Abstract (arXiv) Boundary Representation (B-rep) is the most commonly used data format in Computer-Aided Design (CAD) due to its analytical precision and direct support for parametric editing. However, its heterogeneous structure--continuous parametric geometry combined with discrete topological graphs--poses fundamental challenges for deep learning. Existing methods often predict the heterogeneous B-rep graph directly, using fixed-size padding or sequential tokenization to handle varying primitive counts. These approaches struggle with the combinatorial complexity of CAD models. Furthermore, the discrete, non-differentiable nature of graph data prevents end-to-end optimization of geometry and watertightness. In this work, we introduce DualBrep, a novel continuous representation that unifies B-rep geometry and topology within a fully structured Euclidean domain. DualBrep encodes a CAD model using dual scalar fields: a Signed Distance Function (SDF) representing global shape geometry, and an Unsigned Distance Field (UDF) implicitly encoding topological structure via a Voronoi partitioning of surface elements. Rather than processing these fields independently, we compress them into a single latent space. While the dual-field formulation alone provides a flexible, primitive-free segmentation signal that adapts to arbitrary face counts and surface types, the shared latent makes generation tractable. A Flow Matching model can sample geometry and topology jointly from a single code, avoiding the error accumulation that plagues sequential B-rep predictors. Finally, a neural rebuilder extracts explicit B-rep models--comprising both prismatic and free-form primitives--directly from our continuous dual fields. We demonstrate that DualBrep is a robust backbone for CAD learning, achieving strong performance in point cloud reverse engineering and generative modeling via latent flow matching.