  We study several properties of distillation protocols to purify multilevel
qubit states (qudits) when applied to a certain family of initial mixed
bipartite states. We find that it is possible to use qudits states to increase
the stability region obtained with the flow equations to distill qubits. In
particular, for qutrits we get the phase diagram of the distillation process
with a rich structure of fixed points. We investigate the large-$D$ limit of
qudits protocols and find an analytical solution in the continuum limit. The
general solution of the distillation recursion relations is presented in an
appendix. We stress the notion of weight amplification for distillation
protocols as opposed to the quantum amplitude amplification that appears in the
Grover algorithm. Likewise, we investigate the relations between quantum
distillation and quantum renormalization processes.
