# A Simple Approach to Differentiable Rendering of SDFs

arXiv: https://arxiv.org/abs/2405.08733 · HTML: https://mlsanity.com/paper/2405.08733/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 44 references that are in the map.
- First posted on arXiv 14 May 2024.

## Builds on (most cited first, 23 of 23)

- [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)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [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)
- [PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting](https://mlsanity.com/paper/2104.00674/) (2021)
- [BakedSDF: Meshing Neural SDFs for Real-Time View Synthesis](https://mlsanity.com/paper/2302.14859/) (2023)
- [DIST: Rendering Deep Implicit Signed Distance Function with Differentiable Sphere Tracing](https://mlsanity.com/paper/1911.13225/) (2019)
- [Modeling Indirect Illumination for Inverse Rendering](https://mlsanity.com/paper/2204.06837/) (2022)
- [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020)
- [IRON: Inverse Rendering by Optimizing Neural SDFs and Materials from Photometric Images](https://mlsanity.com/paper/2204.02232/) (2022)
- [Delicate Textured Mesh Recovery from NeRF via Adaptive Surface Refinement](https://mlsanity.com/paper/2303.02091/) (2023)
- [NeRFMeshing: Distilling Neural Radiance Fields into Geometrically-Accurate 3D Meshes](https://mlsanity.com/paper/2303.09431/) (2023)
- [Neural-PBIR Reconstruction of Shape, Material, and Illumination](https://mlsanity.com/paper/2304.13445/) (2023)
- [A Level Set Theory for Neural Implicit Evolution under Explicit Flows](https://mlsanity.com/paper/2204.07159/) (2022)
- [Differentiable Surface Rendering via Non-Differentiable Sampling](https://mlsanity.com/paper/2108.04886/) (2021)
- [Differentiable Rendering of Neural SDFs through Reparameterization](https://mlsanity.com/paper/2206.05344/) (2022)
- [Physics-Based Inverse Rendering using Combined Implicit and Explicit Geometries](https://mlsanity.com/paper/2205.01242/) (2022)
- [Eclipse: Disambiguating Illumination and Materials using Unintended Shadows](https://mlsanity.com/paper/2305.16321/) (2023)

## Built on by (most cited first, 7 of 7)

- [Radiance Surfaces: Optimizing Surface Representations with a 5D Radiance Field Loss](https://mlsanity.com/paper/2501.18627/) (2025)
- [Many-Worlds Inverse Rendering](https://mlsanity.com/paper/2408.16005/) (2024)
- [Neural Geometry Image-Based Representations with Optimal Transport (OT)](https://mlsanity.com/paper/2511.18679/) (2025)
- [Inverse Rendering for High-Genus Surface Meshes from Multi-View Images](https://mlsanity.com/paper/2511.18680/) (2025)
- [Locally Orderless Images for Optimization in Differentiable Rendering](https://mlsanity.com/paper/2503.21931/) (2025)
- [Automated design of compound lenses with discrete-continuous optimization](https://mlsanity.com/paper/2509.23572/) (2025)
- [CubicSplat: Differentiable Vector Graphics via Error-Bounded Forward Relaxation](https://mlsanity.com/paper/2608.20803/) (2026)

## Abstract (arXiv)

We present a simple algorithm for differentiable rendering of surfaces represented by Signed Distance Fields (SDF), which makes it easy to integrate rendering into gradient-based optimization pipelines. To tackle visibility-related derivatives that make rendering non-differentiable, existing physically based differentiable rendering methods often rely on elaborate guiding data structures or reparameterization with a global impact on variance. In this article, we investigate an alternative that embraces nonzero bias in exchange for low variance and architectural simplicity. Our method expands the lower-dimensional boundary integral into a thin band that is easy to sample when the underlying surface is represented by an SDF. We demonstrate the performance and robustness of our formulation in end-to-end inverse rendering tasks, where it obtains results that are competitive with or superior to existing work.