Neural module networks (NMN) are a popular approach for solving multi-modal tasks such as visual question answering (VQA) and visual referring expression recognition (REF). A key limitation in prior implementations of NMN is that the neural modules do not effectively capture the association between the visual input and the relevant neighbourhood context of the textual input. This limits their generalizability. For instance, NMN fail to understand new concepts such as “yellow sphere to the left" even when it is a combination of known concepts from train data: “blue sphere", “yellow cube", and “metallic cube to the left". In this paper, we address this limitation by introducing a language-guided adaptive convolution layer (LG-Conv) into NMN, in which the filter weights of convolutions are explicitly multiplied with a spatially varying language-guided kernel. Our model allows the neural module to adaptively co-attend over potential objects of interest from the visual and textual inputs. Extensive experiments on VQA and REF tasks demonstrate the effectiveness of our approach. Additionally, we propose a new challenging out-of-distribution test split for REF task, which we call C3-Ref+, for explicitly evaluating the NMN’s ability to generalize well to adversarial perturbations and unseen combinations of known concepts. Experiments on C3-Ref+ further demonstrate the generalization capabilities of our approach.