Monte Carlo methods have been widely adopted in physics-based rendering. A key property of a Monte Carlo estimator is its variance, which dictates the convergence rate of the estimator. In this paper, we devise a mathematical formulation for derivatives of rendering variance with respect to not only scene parameters (e.g., surface roughness) but also sampling probabilities. Based on this formulation, we introduce unbiased Monte Carlo estimators for those derivatives. Our theory and algorithm enable variance-aware inverse rendering which alters a virtual scene and/or an estimator in an optimal way to offer a good balance between bias and variance. We evaluate our technique using several synthetic examples.

• Paper: pdf (18 MB)
• Source code: coming soon.

@inproceedings{Yan:2024:PSDR-Var,
  title={Differentiating Variance for Variance-Aware Inverse Rendering},
  author={Yan, K. and Pegoraro, V. and Droske, M. and Vorba, J. and Zhao, S.},
  booktitle = {ACM SIGGRAPH Asia 2024 Conference Proceedings},
  year = {2024},
}

We would like to thank Qianhui Wu for her artistic support in this work and Weizhen Huang discussions related to the rendering process. This work started when Kai Yan was an intern at Wētā FX.