Integrated circuit nonvolatile memory devices are manufactured by forming a variable resistance layer on an integrated circuit substrate. The variable resistance layer includes grains that define grain boundaries between the grains. Conductive filaments are formed along at least some of the grain boundaries. Electrodes are formed on the variable resistance layer. The conductive filaments may be formed by implanting conductive ions into at least some of the grain boundaries. Moreover, the variable resistance layer may be a variable resistance oxide of a metal, and the conductive filaments may be the metal. Related devices are also disclosed.