Monte Carlo rendering often faces a dilemma, namely, whether to choose an unbiased estimator or a biased one. Although different integrators have been developed to address various scenarios, no single method can effectively manage all situations. Thus, finding a good approach to combine different integrators has always been a topic that warrants exploration. This work proposes DSCombiner, a new shrinkage estimator that flexibly combines unbiased and biased estimators (typically generated by different integrators) in image space into a single estimating procedure, strategically utilizing the strengths of different integrators while minimizing their weaknesses. DSCombiner overcomes the limitation of single shrinkage combiners by introducing a two-step shrinkage towards a noise-free radiance prior. We derive optimal shrinkage factors for the two steps within a hierarchical Bayesian framework, and provide a deep learning-based method to improve the results. Comprehensive qualitative and quantitative validations across diverse scenes demonstrate visible improvements in image quality, as compared with previous image-space and path-space combiners.

The efficiency of inverse optimization in physically based differentiable rendering heavily depends on the variance of Monte Carlo estimation. Despite recent advancements emphasizing the necessity of tailored differential sampling strategies, the general approaches remain unexplored. In this paper, we investigate the interplay between local sampling decisions and the estimation of light path derivatives. Considering that modern differentiable rendering algorithms share the same path for estimating differential radiance and ordinary radiance, we demonstrate that conventional guiding approaches, conditioned solely on the last vertex, cannot attain this density. Instead, a mixture of different sampling distributions is required, where the weights are conditioned on all the previously sampled vertices in the path. To embody our theory, we implement a conditional mixture path guiding that explicitly computes optimal weights on the fly. Furthermore, we show how to perform positivization to eliminate sign variance and extend to scenes with millions of parameters. To the best of our knowledge, this is the first generic framework for applying path guiding to differentiable rendering. Extensive experiments demonstrate that our method achieves nearly one order of magnitude improvements over state-of-the-art methods in terms of variance reduction in gradient estimation and errors of inverse optimization. The implementation of our proposed method is available at https://github.com/mollnn/conditional-mixture.