A relation exists between network proximity of molecular entities in interaction networks, functional similarity and association with diseases. The identification of network regions associated with biological functions and pathologies is a major goal in systems biology. We describe a network diffusion-based pipeline for the interpretation of different types of omics in the context of molecular interaction networks. We introduce the network smoothing index, a network-based quantity that allows to jointly quantify the amount of omics information in genes and in their network neighbourhood, using network diffusion to define network proximity. The approach is applicable to both descriptive and inferential statistics calculated on omics data. We also show that network resampling, applied to gene lists ranked by quantities derived from the network smoothing index, indicates the presence of significantly connected genes. As a proof of principle, we identified gene modules enriched in somatic mutations and transcriptional variations observed in samples of prostate adenocarcinoma (PRAD). In line with the local hypothesis, network smoothing index and network resampling underlined the existence of a connected component of genes harbouring molecular alterations in PRAD.