Monte Carlo integration is an efficient method to solve a high-dimensional integral in light transport simulation, but it typically produces noisy images due to its stochastic nature. Many existing methods, such as image denoising and gradient-domain reconstruction, aim to mitigate this noise by introducing some form of correlation among pixels. While those existing methods reduce noise, they are known to still suffer from method-specific residual noise or systematic errors. We propose a unified framework that reduces such remaining errors. Our framework takes a pair of images, one with independent estimates, and the other with the corresponding correlated estimates. Correlated pixel estimates are generated by various existing methods such as denoising and gradient-domain rendering. Our framework then combines the two images via a novel combination kernel.We model our combination kernel as a weighting function with a deep neural network that exploits the correlation among pixel estimates. To improve the robustness of our framework for outliers, we additionally propose an extension to handle multiple image buffers. The results demonstrate that our unified framework can successfully reduce the error of existing methods while treating them as black-boxes.