Integrating structural information and metadata, such as gender, social status, or interests, enriches networks and enables a better understanding of the large-scale structure of complex systems. However, existing approaches to metadata integration only consider immediately adjacent nodes, thus failing to identify and exploit long-range correlations between metadata and network structure, typical of many spatial and social systems. Here we show how a flow-based community-detection approach can integrate network information and distant metadata, providing a more nuanced picture of network structure and correlations. We analyse social and spatial networks using the map equation framework and find that our methodology can detect a variety of useful metadata-informed partitions in diverse real-world systems. This framework paves the way for systematically incorporating metadata in network analysis.