# D2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts

arXiv: https://arxiv.org/abs/2301.11497 · HTML: https://mlsanity.com/paper/2301.11497/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 57 references that are in the map.
- First posted on arXiv 27 Jan 2023.

## Builds on (most cited first, 30 of 45)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [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)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [PartNet: A Large-scale Benchmark for Fine-grained and Hierarchical Part-level 3D Object Understanding](https://mlsanity.com/paper/1812.02713/) (2018)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [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)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [SkexGen: Autoregressive Generation of CAD Construction Sequences with Disentangled Codebooks](https://mlsanity.com/paper/2207.04632/) (2022)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [CSGNet: Neural Shape Parser for Constructive Solid Geometry](https://mlsanity.com/paper/1712.08290/) (2017)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [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)
- [Write, Execute, Assess: Program Synthesis with a REPL](https://mlsanity.com/paper/1906.04604/) (2019)
- [Supervised Fitting of Geometric Primitives to 3D Point Clouds](https://mlsanity.com/paper/1811.08988/) (2018)
- [UCSG-Net -- Unsupervised Discovering of Constructive Solid Geometry Tree](https://mlsanity.com/paper/2006.09102/) (2020)
- [JoinABLe: Learning Bottom-up Assembly of Parametric CAD Joints](https://mlsanity.com/paper/2111.12772/) (2021)
- [3D-PRNN: Generating Shape Primitives with Recurrent Neural Networks](https://mlsanity.com/paper/1708.01648/) (2017)
- [Learning to Infer and Execute 3D Shape Programs](https://mlsanity.com/paper/1901.02875/) (2019)
- [SketchGen: Generating Constrained CAD Sketches](https://mlsanity.com/paper/2106.02711/) (2021)
- [CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly](https://mlsanity.com/paper/2104.05652/) (2021)
- [Point2Cyl: Reverse Engineering 3D Objects from Point Clouds to Extrusion Cylinders](https://mlsanity.com/paper/2112.09329/) (2021)

## Built on by (most cited first, 30 of 40)

- [CAD-MLLM: Unifying Multimodality-Conditioned CAD Generation With MLLM](https://mlsanity.com/paper/2411.04954/) (2024)
- [CAD-Recode: Reverse Engineering CAD Code from Point Clouds](https://mlsanity.com/paper/2412.14042/) (2024)
- [CAD-SIGNet: CAD Language Inference from Point Clouds using Layer-wise Sketch Instance Guided Attention](https://mlsanity.com/paper/2402.17678/) (2024)
- [Text-to-CAD Generation Through Infusing Visual Feedback in Large Language Models](https://mlsanity.com/paper/2501.19054/) (2025)
- [Img2CAD: Conditioned 3D CAD Model Generation from Single Image with Structured Visual Geometry](https://mlsanity.com/paper/2410.03417/) (2024)
- [Img2CAD: Reverse Engineering 3D CAD Models from Images through VLM-Assisted Conditional Factorization](https://mlsanity.com/paper/2408.01437/) (2024)
- [FlexCAD: Unified and Versatile Controllable CAD Generation with Fine-tuned Large Language Models](https://mlsanity.com/paper/2411.05823/) (2024)
- [HoLa: B-Rep Generation using a Holistic Latent Representation](https://mlsanity.com/paper/2504.14257/) (2025)
- [TransCAD: A Hierarchical Transformer for CAD Sequence Inference from Point Clouds](https://mlsanity.com/paper/2407.12702/) (2024)
- [Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning](https://mlsanity.com/paper/2406.05261/) (2024)
- [AutoBrep: Autoregressive B-Rep Generation with Unified Topology and Geometry](https://mlsanity.com/paper/2512.03018/) (2025)
- [cadrille: Multi-modal CAD Reconstruction with Reinforcement Learning](https://mlsanity.com/paper/2505.22914/) (2025)
- [From 2D CAD Drawings to 3D Parametric Models: A Vision-Language Approach](https://mlsanity.com/paper/2412.11892/) (2024)
- [Doodle Your 3D: From Abstract Freehand Sketches to Precise 3D Shapes](https://mlsanity.com/paper/2312.04043/) (2023)
- [BrepGPT: Autoregressive B-rep Generation with Voronoi Half-Patch](https://mlsanity.com/paper/2511.22171/) (2025)
- [Pointer-CAD: Unifying B-Rep and Command Sequences via Pointer-based Edges & Faces Selection](https://mlsanity.com/paper/2603.04337/) (2026)
- [CAD-Judge: Toward Efficient Morphological Grading and Verification for Text-to-CAD Generation](https://mlsanity.com/paper/2508.04002/) (2025)
- [Learning to Edit Visual Programs with Self-Supervision](https://mlsanity.com/paper/2406.02383/) (2024)
- [CADReasoner: Iterative Program Editing for CAD Reverse Engineering](https://mlsanity.com/paper/2603.29847/) (2026)
- [DPA-Net: Structured 3D Abstraction from Sparse Views via Differentiable Primitive Assembly](https://mlsanity.com/paper/2404.00875/) (2024)
- [ContrastCAD: Contrastive Learning-based Representation Learning for Computer-Aided Design Models](https://mlsanity.com/paper/2404.01645/) (2024)
- [SweepNet: Unsupervised Learning Shape Abstraction via Neural Sweepers](https://mlsanity.com/paper/2407.06305/) (2024)
- [GeoCAD: Local Geometry-Controllable CAD Generation with Large Language Models](https://mlsanity.com/paper/2506.10337/) (2025)
- [MiCADangelo: Fine-Grained Reconstruction of Constrained CAD Models from 3D Scans](https://mlsanity.com/paper/2510.23429/) (2025)
- [Concise Plane Arrangements for Low-Poly Surface and Volume Modelling](https://mlsanity.com/paper/2404.06154/) (2024)
- [Can AI Understand the Language of Origami?](https://mlsanity.com/paper/2603.13856/) (2026)
- [MV2Cyl: Reconstructing 3D Extrusion Cylinders from Multi-View Images](https://mlsanity.com/paper/2406.10853/) (2024)
- [CropCraft: Complete Structural Characterization of Crop Plants From Images](https://mlsanity.com/paper/2411.09693/) (2024)
- [CADKnitter: Compositional CAD Generation from Text and Geometry Guidance](https://mlsanity.com/paper/2512.11199/) (2025)
- [Autoregressive B-Rep Shape Generation with Parametric Surfaces](https://mlsanity.com/paper/2607.17093/) (2026)

## Abstract (arXiv)

We present D2CSG, a neural model composed of two dual and complementary network branches, with dropouts, for unsupervised learning of compact constructive solid geometry (CSG) representations of 3D CAD shapes. Our network is trained to reconstruct a 3D shape by a fixed-order assembly of quadric primitives, with both branches producing a union of primitive intersections or inverses. A key difference between D2CSG and all prior neural CSG models is its dedicated residual branch to assemble the potentially complex shape complement, which is subtracted from an overall shape modeled by the cover branch. With the shape complements, our network is provably general, while the weight dropout further improves compactness of the CSG tree by removing redundant primitives. We demonstrate both quantitatively and qualitatively that D2CSG produces compact CSG reconstructions with superior quality and more natural primitives than all existing alternatives, especially over complex and high-genus CAD shapes.