# Differentiable Voxelization of Surface Representations

arXiv: https://arxiv.org/abs/2608.15934 · HTML: https://mlsanity.com/paper/2608.15934/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 71 references that are in the map.
- First posted on arXiv 16 Aug 2026.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Voxel R-CNN: Towards High Performance Voxel-based 3D Object Detection](https://mlsanity.com/paper/2012.15712/) (2020)
- [Resolving 3D Human Pose Ambiguities with 3D Scene Constraints](https://mlsanity.com/paper/1908.06963/) (2019)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Coherent Reconstruction of Multiple Humans from a Single Image](https://mlsanity.com/paper/2006.08586/) (2020)
- [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020)
- [Learning Signed Distance Field for Multi-view Surface Reconstruction](https://mlsanity.com/paper/2108.09964/) (2021)
- [Scalable Differentiable Physics for Learning and Control](https://mlsanity.com/paper/2007.02168/) (2020)
- [Differentiable Physics Simulation of Dynamics-Augmented Neural Objects](https://mlsanity.com/paper/2210.09420/) (2022)
- [ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generators](https://mlsanity.com/paper/2108.09432/) (2021)
- [Cubic Stylization](https://mlsanity.com/paper/1910.02926/) (2019)
- [Geometry in Style: 3D Stylization via Surface Normal Deformation](https://mlsanity.com/paper/2503.23241/) (2025)
- [3D Reconstruction with Fast Dipole Sums](https://mlsanity.com/paper/2405.16788/) (2024)
- [DiffCSG: Differentiable CSG via Rasterization](https://mlsanity.com/paper/2409.01421/) (2024)
- [TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2505.04590/) (2025)
- [Hand-Shadow Poser](https://mlsanity.com/paper/2505.07012/) (2025)
- [Differentiable Voxelization and Mesh Morphing](https://mlsanity.com/paper/2407.11272/) (2024)
- [WindPoly: Polygonal Mesh Reconstruction via Winding Numbers](https://mlsanity.com/paper/2407.19208/) (2024)

## Abstract (arXiv)

Different shape representations facilitate different computations. Surface representations, in particular meshes, are often used for modeling, whereas volume representations are useful for spatial queries such as intersection or containment. Optimizing a surface representation based on a volumetric properties by gradient descent requires the derivatives of the volume relative to its bounding surface. We derive this gradient for winding numbers and show that it can be efficiently computed for volumetric values sampled on a regular grid (voxel representation) and surface parameters based on vertex sets (triangle meshes). This enables an efficient solution for a variety of optimization problems. We demonstrate the practical use of this approach at the examples of deforming meshes to resolve intersections, being manufacturable by cutting with a bandsaw from three directions, and creating shapes that are close to tiling 3D space.