Most object detection systems consist of three stages. First, a set of individual hypotheses for object locations is generated using a proposal generating algorithm. Second, a classifier scores every generated hypothesis independently to obtain a multi-class prediction. Finally, all scored hypotheses are filtered via a non-differentiable and decoupled non-maximum suppression (NMS) post-processing step. In this paper, we propose a filtering network (FNet), a method which replaces NMS with a differentiable neural network that allows joint reasoning and re-scoring of the generated set of hypotheses per image. This formulation enables end-to-end training of the full object detection pipeline. First, we demonstrate that FNet, a feed-forward network architecture, is able to mimic NMS decisions, despite the sequential nature of NMS. We further analyze NMS failures and propose a loss formulation that is better aligned with the mean average precision (mAP) evaluation metric. We evaluate FNet on several standard detection datasets. Results surpass standard NMS on highly occluded settings of a synthetic overlapping MNIST dataset and show competitive behavior on PascalVOC2007 and KITTI detection benchmarks.