  We introduce a single generative mechanism with which it is able to describe
diverse non-stationary diffusions. A non-stationary Markovian replication
process for steps is considered, for which we analytically derive
time-evolution of the probability distribution of the walker's displacement and
the generalized telegrapher equation with time-varying coefficients, and find
that diffusivity can be determined by temporal changes of replication of a
immediate step. By controlling the replications, we realize the diverse
diffusions such as alternating diffusions, superdiffusions, subdiffusions, and
marginal diffusions which are originated from oscillating,
increasing,decreasing, and slowly increasing or decreasing replications with
time, respectively.
