We propose a deep-learning method for automatically decomposing noisy Monte Carlo renderings into components that kernelpredicting denoisers can denoise more effectively. In our model, a neural decomposition module learns to predict noisy components and corresponding feature maps, which are consecutively reconstructed by a denoising module. The components are predicted based on statistics aggregated at the pixel level by the renderer. Denoising these components individually allows the use of per-component kernels that adapt to each component's noisy signal characteristics. Experimentally, we show that the proposed decomposition module consistently improves the denoising quality of current state-of-the-art kernel-predicting denoisers on large-scale academic and production datasets.