Recursive Control Variates for Inverse Rendering

We present a method for reducing errors---variance and bias---in physically based differentiable rendering (PBDR). Typical applications of PBDR repeatedly render a scene as part of an optimization loop involving gradient descent. The actual change introduced by each gradient descent step is often relatively small, causing a significant degree of redundancy in this computation. We exploit this redundancy by formulating a gradient estimator that employs a \emph{recursive control variate}, which leverages information from previous optimization steps. The control variate reduces variance in gradients, and, perhaps more importantly, alleviates issues that arise from differentiating %non-$\L^2$ loss functions with respect to noisy inputs, a common cause of drift to bad local minima or divergent optimizations. We experimentally evaluate our approach on a variety of path-traced scenes containing surfaces and volumes and observe that primal rendering efficiency improves by a factor of up to 10.