Acoustic beamformers have been widely used to enhance audio signals. The best current methods are DNN-powered variants of the generalized eigenvalue beamformer, and DNN-based filterestimation methods that directly compute beamforming filters. Both approaches, while effective, have blindspots in their generalizability. We propose a novel approach that combines both approaches into a single framework that attempts to exploit the best features of both. The resulting model, called a W-Net beamformer, includes two components: the first computes a noise-masked reference which the second uses to estimate beamforming filters. Results on data that include a wide variety of room and noise conditions, including static and mobile noise sources, show that the proposed beamformer outperforms other methods in all tested evaluation metrics.