# Differentiable Surface Rendering via Non-Differentiable Sampling

arXiv: https://arxiv.org/abs/2108.04886 · HTML: https://mlsanity.com/paper/2108.04886/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 10 Aug 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [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)
- [Softmax Splatting for Video Frame Interpolation](https://mlsanity.com/paper/2003.05534/) (2020)
- [Differentiable Surface Splatting for Point-based Geometry Processing](https://mlsanity.com/paper/1906.04173/) (2019)
- [Learning to Predict 3D Objects with an Interpolation-based Differentiable Renderer](https://mlsanity.com/paper/1908.01210/) (2019)
- [DIST: Rendering Deep Implicit Signed Distance Function with Differentiable Sphere Tracing](https://mlsanity.com/paper/1911.13225/) (2019)
- [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020)
- [Learning single-image 3D reconstruction by generative modelling of shape, pose and shading](https://mlsanity.com/paper/1901.06447/) (2019)
- [A Versatile Scene Model with Differentiable Visibility Applied to Generative Pose Estimation](https://mlsanity.com/paper/1602.03725/) (2016)

## Built on by (most cited first, 28 of 28)

- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [Hallucinated Neural Radiance Fields in the Wild](https://mlsanity.com/paper/2111.15246/) (2021)
- [NeSF: Neural Semantic Fields for Generalizable Semantic Segmentation of 3D Scenes](https://mlsanity.com/paper/2111.13260/) (2021)
- [FENeRF: Face Editing in Neural Radiance Fields](https://mlsanity.com/paper/2111.15490/) (2021)
- [IRON: Inverse Rendering by Optimizing Neural SDFs and Materials from Photometric Images](https://mlsanity.com/paper/2204.02232/) (2022)
- [GOI: Find 3D Gaussians of Interest with an Optimizable Open-vocabulary Semantic-space Hyperplane](https://mlsanity.com/paper/2405.17596/) (2024)
- [Approximate Differentiable Rendering with Algebraic Surfaces](https://mlsanity.com/paper/2207.10606/) (2022)
- [A Level Set Theory for Neural Implicit Evolution under Explicit Flows](https://mlsanity.com/paper/2204.07159/) (2022)
- [NeRFLiX: High-Quality Neural View Synthesis by Learning a Degradation-Driven Inter-viewpoint MiXer](https://mlsanity.com/paper/2303.06919/) (2023)
- [Differentiable Rendering of Neural SDFs through Reparameterization](https://mlsanity.com/paper/2206.05344/) (2022)
- [Re-ReND: Real-time Rendering of NeRFs across Devices](https://mlsanity.com/paper/2303.08717/) (2023)
- [Neural Parameterization for Dynamic Human Head Editing](https://mlsanity.com/paper/2207.00210/) (2022)
- [CCL-LGS: Contrastive Codebook Learning for 3D Language Gaussian Splatting](https://mlsanity.com/paper/2505.20469/) (2025)
- [Spelunking the Deep: Guaranteed Queries on General Neural Implicit Surfaces via Range Analysis](https://mlsanity.com/paper/2202.02444/) (2022)
- [Dr.Hair: Reconstructing Scalp-Connected Hair Strands without Pre-training via Differentiable Rendering of Line Segments](https://mlsanity.com/paper/2403.17496/) (2024)
- [Plateau-reduced Differentiable Path Tracing](https://mlsanity.com/paper/2211.17263/) (2022)
- [Canonical Factors for Hybrid Neural Fields](https://mlsanity.com/paper/2308.15461/) (2023)
- [From NeRFLiX to NeRFLiX++: A General NeRF-Agnostic Restorer Paradigm](https://mlsanity.com/paper/2306.06388/) (2023)
- [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)
- [Benchmarking Implicit Neural Representation and Geometric Rendering in Real-Time RGB-D SLAM](https://mlsanity.com/paper/2403.19473/) (2024)
- [FLNeRF: 3D Facial Landmarks Estimation in Neural Radiance Fields](https://mlsanity.com/paper/2211.11202/) (2022)
- [FastMESH: Fast Surface Reconstruction by Hexagonal Mesh-based Neural Rendering](https://mlsanity.com/paper/2305.17858/) (2023)
- [GET3D--: Learning GET3D from Unconstrained Image Collections](https://mlsanity.com/paper/2307.14918/) (2023)
- [High-Quality Real-Time Rendering Using Subpixel Sampling Reconstruction](https://mlsanity.com/paper/2301.01036/) (2023)
- [DR-WLC: Dimensionality Reduction cognition for object detection and pose estimation by Watching, Learning and Checking](https://mlsanity.com/paper/2301.06944/) (2023)
- [Deep Neural Implicit Representation of Accessibility for Multi-Axis Manufacturing](https://mlsanity.com/paper/2409.02115/) (2024)
- [VEPHand: View-Efficient Photometric Hand Performance Capture at Scale](https://mlsanity.com/paper/2606.15966/) (2026)

## Abstract (arXiv)

We present a method for differentiable rendering of 3D surfaces that supports both explicit and implicit representations, provides derivatives at occlusion boundaries, and is fast and simple to implement. The method first samples the surface using non-differentiable rasterization, then applies differentiable, depth-aware point splatting to produce the final image. Our approach requires no differentiable meshing or rasterization steps, making it efficient for large 3D models and applicable to isosurfaces extracted from implicit surface definitions. We demonstrate the effectiveness of our method for implicit-, mesh-, and parametric-surface-based inverse rendering and neural-network training applications. In particular, we show for the first time efficient, differentiable rendering of an isosurface extracted from a neural radiance field (NeRF), and demonstrate surface-based, rather than volume-based, rendering of a NeRF.