Path-Space Differentiable Rendering
Cheng Zhang1, Bailey Miller2, Kai Yan1, Ioannis Gkioulekas2, and Shuang Zhao1
1University of California, Irvine     2Carnegie Mellon University
ACM Transactions on Graphics (SIGGRAPH 2020), 39(4), 2020

Physics-based differentiable rendering, the estimation of derivatives of radiometric measures with respect to arbitrary scene parameters, has a diverse array of applications from solving analysis-by-synthesis problems to training machine learning pipelines incorporating forward rendering processes. Unfortunately, general-purpose differentiable rendering remains challenging due to the lack of efficient estimators as well as the need to identify and handle complex discontinuities such as visibility boundaries. In this paper, we show how path integrals can be differentiated with respect to arbitrary differentiable changes of a scene. We provide a detailed theoretical analysis of this process and establish new differentiable rendering formulations based on the resulting differential path integrals. Our path-space differentiable rendering formulation allows the design of new Monte Carlo estimators that offer significantly better efficiency than state-of-the-art methods in handling complex geometric discontinuities and light transport phenomena such as caustics.

We validate our method by comparing our derivative estimates to those generated using the finite-difference method. To demonstrate the effectiveness of our technique, we compare inverse-rendering performance with a few state-of-the-art differentiable rendering methods.

Talk recording
  • Paper: pdf (45 MB)
  • Talk slides: pptx (112 MB)
  • Supplemental document: pdf (0.5 MB)
  • Supplemental material: html, zip (231 MB)
  • Code: zip (CPU-based, 0.7 MB); coming soon! (GPU-based)
Bibtex citation
  title={Path-Space Differentiable Rendering},
  author={Zhang, Cheng and Miller, Bailey and Yan, Kai and Gkioulekas, Ioannis and Zhao, Shuang},
  journal={ACM Trans. Graph.},

We thank the anonymous reviewers for their constructive comments. This work was supported by NSF grants 1730147, 1900849 and 1900927, as well as a gift from the AWS Cloud Credits for Research program.