# DMesh: A Differentiable Mesh Representation

arXiv: https://arxiv.org/abs/2404.13445 · HTML: https://mlsanity.com/paper/2404.13445/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 20 Apr 2024.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [Extracting Triangular 3D Models, Materials, and Lighting From Images](https://mlsanity.com/paper/2111.12503/) (2021)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [Learning to Predict 3D Objects with an Interpolation-based Differentiable Renderer](https://mlsanity.com/paper/1908.01210/) (2019)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [NeuralUDF: Learning Unsigned Distance Fields for Multi-view Reconstruction of Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2211.14173/) (2022)
- [Fully Convolutional Mesh Autoencoder using Efficient Spatially Varying Kernels](https://mlsanity.com/paper/2006.04325/) (2020)
- [A Level Set Theory for Neural Implicit Evolution under Explicit Flows](https://mlsanity.com/paper/2204.07159/) (2022)
- [NeUDF: Leaning Neural Unsigned Distance Fields with Volume Rendering](https://mlsanity.com/paper/2304.10080/) (2023)
- [NeuManifold: Neural Watertight Manifold Reconstruction with Efficient and High-Quality Rendering Support](https://mlsanity.com/paper/2305.17134/) (2023)
- [Ghost on the Shell: An Expressive Representation of General 3D Shapes](https://mlsanity.com/paper/2310.15168/) (2023)
- [DeepMesh: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2106.11795/) (2021)
- [Differentiable Surface Triangulation](https://mlsanity.com/paper/2109.10695/) (2021)

## Built on by (most cited first, 9 of 9)

- [SparseFlex: High-Resolution and Arbitrary-Topology 3D Shape Modeling](https://mlsanity.com/paper/2503.21732/) (2025)
- [ARMesh: Autoregressive Mesh Generation via Next-Level-of-Detail Prediction](https://mlsanity.com/paper/2509.20824/) (2025)
- [LATO.2: Factorized 3D Mesh Generation with Vertex and Topology Flow](https://mlsanity.com/paper/2607.10623/) (2026)
- [Triangle Splatting+: Differentiable Rendering with Opaque Triangles](https://mlsanity.com/paper/2509.25122/) (2025)
- [From Blobs to Spokes: High-Fidelity Surface Reconstruction via Oriented Gaussians](https://mlsanity.com/paper/2604.07337/) (2026)
- [ExMesh: Explicit Mesh Reconstruction with Topology Adaptation](https://mlsanity.com/paper/2606.07288/) (2026)
- [PolyFlow: Continuous Topology Embedding Flow Matching for Artist-style Mesh Generation](https://mlsanity.com/paper/2606.30673/) (2026)
- [DiffTrans: Differentiable Geometry-Materials Decomposition for Reconstructing Transparent Objects](https://mlsanity.com/paper/2603.00413/) (2026)
- [DiffGI: Differentiable Geometry Images for High-Fidelity Thin-Shell 3D Generation](https://mlsanity.com/paper/2607.13365/) (2026)

## Abstract (arXiv)

We present a differentiable representation, DMesh, for general 3D triangular meshes. DMesh considers both the geometry and connectivity information of a mesh. In our design, we first get a set of convex tetrahedra that compactly tessellates the domain based on Weighted Delaunay Triangulation (WDT), and select triangular faces on the tetrahedra to define the final mesh. We formulate probability of faces to exist on the actual surface in a differentiable manner based on the WDT. This enables DMesh to represent meshes of various topology in a differentiable way, and allows us to reconstruct the mesh under various observations, such as point cloud and multi-view images using gradient-based optimization. The source code and full paper is available at: https://sonsang.github.io/dmesh-project.