A cellular sheaf on a simplicial complex assigns a vector space (stalk) to each cell and linear maps (restriction maps) relating adjacent cells. The sheaf Laplacian L = B^T B generalizes the graph Laplacian: its kernel (global sections) captures signals that are consistent across all restriction maps simultaneously. Sheaf diffusion (Hansen & Ghrist, 2021) runs the heat equation on sheaf data, smoothing signals toward global sections while respecting the local geometric constraints encoded by restriction maps. Applications span multi-modal data fusion, opinion dynamics with stubborn agents, and learning on heterogeneous information networks where different node types carry different signal types.