By using the worldline approach to quantum field theory, we demonstrate to all orders that the sources of a quantum field theory over Mink$_4$ naturally form a field theory over AdS$_5$. In particular, this holds for higher-spin sources of a free scalar theory. We work entirely within quantum-field theory and do not select a subset of diagrams. As auxiliary fifth dimension Schwinger's proper time is grouped with the physical four spacetime dimensions into an AdS$_5$ geometry. The four-dimensional sources are extended to five-dimensional fields by a Wilson flow (gradient flow). A variational principle for said flow reproduces the corresponding holographic computation.