Understanding how the anatomy of the human brain constrains and influences the formation of large-scale functional networks remains a fundamental question in neuroscience. Here, given measured brain activity in gray matter, we interpolate these functional signals into the white matter on a structurally-informed high-resolution voxel-level brain grid. The interpolated volumes reflect the underlying anatomical information, revealing white matter structures that mediate the interaction between temporally coherent gray matter regions. Functional connectivity analyses of the interpolated volumes reveal an enriched picture of the default mode network (DMN) and its subcomponents, including the different white matter bundles that are implicated in their formation, thus extending currently known spatial patterns that are limited within the gray matter only. These subcomponents have distinct structure-function patterns, each of which are differentially observed during tasks, demonstrating plausible structural mechanisms for functional switching between task-positive and -negative components. This work opens new avenues for the integration of brain structure and function, and demonstrates the collective mediation of white matter pathways across short and long-distance functional connections.