# Differentiable Rendering of Neural SDFs through Reparameterization

arXiv: https://arxiv.org/abs/2206.05344 · HTML: https://mlsanity.com/paper/2206.05344/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 59 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 21 of 21)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting](https://mlsanity.com/paper/2104.00674/) (2021)
- [Neural Reflectance Fields for Appearance Acquisition](https://mlsanity.com/paper/2008.03824/) (2020)
- [Neural Volumes: Learning Dynamic Renderable Volumes from Images](https://mlsanity.com/paper/1906.07751/) (2019)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020)
- [Neural Lumigraph Rendering](https://mlsanity.com/paper/2103.11571/) (2021)
- [Deep Reflectance Volumes: Relightable Reconstructions from Multi-View Photometric Images](https://mlsanity.com/paper/2007.09892/) (2020)
- [A Versatile Scene Model with Differentiable Visibility Applied to Generative Pose Estimation](https://mlsanity.com/paper/1602.03725/) (2016)
- [Differentiable Surface Rendering via Non-Differentiable Sampling](https://mlsanity.com/paper/2108.04886/) (2021)
- [Differentiable Visual Computing](https://mlsanity.com/paper/1904.12228/) (2019)

## Built on by (most cited first, 26 of 26)

- [Neural-PBIR Reconstruction of Shape, Material, and Illumination](https://mlsanity.com/paper/2304.13445/) (2023)
- [IllumiNeRF: 3D Relighting Without Inverse Rendering](https://mlsanity.com/paper/2406.06527/) (2024)
- [Factorized Inverse Path Tracing for Efficient and Accurate Material-Lighting Estimation](https://mlsanity.com/paper/2304.05669/) (2023)
- [ShadowNeuS: Neural SDF Reconstruction by Shadow Ray Supervision](https://mlsanity.com/paper/2211.14086/) (2022)
- [Eclipse: Disambiguating Illumination and Materials using Unintended Shadows](https://mlsanity.com/paper/2305.16321/) (2023)
- [Rasterized Edge Gradients: Handling Discontinuities Differentiably](https://mlsanity.com/paper/2405.02508/) (2024)
- [NeRF as a Non-Distant Environment Emitter in Physics-based Inverse Rendering](https://mlsanity.com/paper/2402.04829/) (2024)
- [HotSpot: Signed Distance Function Optimization with an Asymptotically Sufficient Condition](https://mlsanity.com/paper/2411.14628/) (2024)
- [A Simple Approach to Differentiable Rendering of SDFs](https://mlsanity.com/paper/2405.08733/) (2024)
- [DiffCSG: Differentiable CSG via Rasterization](https://mlsanity.com/paper/2409.01421/) (2024)
- [A Theory of Topological Derivatives for Inverse Rendering of Geometry](https://mlsanity.com/paper/2308.09865/) (2023)
- [3D Neural Sculpting (3DNS): Editing Neural Signed Distance Functions](https://mlsanity.com/paper/2209.13971/) (2022)
- [Differentiable Shadow Mapping for Efficient Inverse Graphics](https://mlsanity.com/paper/2308.10896/) (2023)
- [DiffSoup: Direct Differentiable Rasterization of Triangle Soup for Extreme Radiance Field Simplification](https://mlsanity.com/paper/2603.27151/) (2026)
- [A Review of Deep Learning-Powered Mesh Reconstruction Methods](https://mlsanity.com/paper/2303.02879/) (2023)
- [PG-NeuS: Robust and Efficient Point Guidance for Multi-View Neural Surface Reconstruction](https://mlsanity.com/paper/2310.07997/) (2023)
- [Many-Worlds Inverse Rendering](https://mlsanity.com/paper/2408.16005/) (2024)
- [RNA: Relightable Neural Assets](https://mlsanity.com/paper/2312.09398/) (2023)
- [Single-view 3D reconstruction via inverse procedural modeling](https://mlsanity.com/paper/2310.13373/) (2023)
- [Weakly-Supervised 3D Reconstruction of Clothed Humans via Normal Maps](https://mlsanity.com/paper/2311.16042/) (2023)
- [Differentiable Convex Polyhedra Optimization from Multi-view Images](https://mlsanity.com/paper/2407.15686/) (2024)
- [Interactive Stroke-based Neural SDF Sculpting](https://mlsanity.com/paper/2502.02891/) (2025)
- [Probabilistic Directed Distance Fields for Ray-Based Shape Representations](https://mlsanity.com/paper/2404.09081/) (2024)
- [Physically Plausible Human-Object Rendering from Sparse Views via 3D Gaussian Splatting](https://mlsanity.com/paper/2503.09640/) (2025)
- [Automated design of compound lenses with discrete-continuous optimization](https://mlsanity.com/paper/2509.23572/) (2025)
- [GradInf: Gradient Estimation as Probabilistic Inference](https://mlsanity.com/paper/2607.07840/) (2026)

## Abstract (arXiv)

We present a method to automatically compute correct gradients with respect to geometric scene parameters in neural SDF renderers. Recent physically-based differentiable rendering techniques for meshes have used edge-sampling to handle discontinuities, particularly at object silhouettes, but SDFs do not have a simple parametric form amenable to sampling. Instead, our approach builds on area-sampling techniques and develops a continuous warping function for SDFs to account for these discontinuities. Our method leverages the distance to surface encoded in an SDF and uses quadrature on sphere tracer points to compute this warping function. We further show that this can be done by subsampling the points to make the method tractable for neural SDFs. Our differentiable renderer can be used to optimize neural shapes from multi-view images and produces comparable 3D reconstructions to recent SDF-based inverse rendering methods, without the need for 2D segmentation masks to guide the geometry optimization and no volumetric approximations to the geometry.