Lattice field theory is embedded in ultraviolet-finite continuum theory by transforming a finite number of continuum degrees of freedom into lattice degrees of freedom. The resulting Hamiltonian is equivalent to the continuum Hamiltonian, and consists of the lattice Hamiltonian plus corrections. At zero lattice spacing the corrections vanish and the lattice Hamiltonian has finite matrix elements. At finite spacing there is a simple estimate of the discrepancy between lattice and continuum field theories, and more exact calculations are outlined. A strategy is sketched for using lattice methods to calculate in continuum field theory.