We present a model-based method for inferring full-brain neural activity at millimeter-scale spatial resolutions and millisecond-scale temporal resolutions using standard human intracranial recordings. Our approach makes the simplifying assumptions that different people’s brains exhibit similar correlational structure, and that activity and correlation patterns vary smoothly over space. One can then ask, for an arbitrary individual’s brain: given recordings from a limited set of locations in that individual’s brain, along with the observed spatial correlations learned from other people’s recordings, how much can be inferred about ongoing activity at other locations throughout that individual’s brain? We show that our approach generalizes across people and tasks, thereby providing a person- and task-general means of inferring high spatiotemporal resolution full-brain neural dynamics from standard low-density intracranial recordings.