Differentiating Variance for Variance-Aware Inverse Rendering

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.