  We present parameter-free tunneling calculations for various cluster
radioactivities including the diproton decays of atomic nuclei. An uniform
folded cluster potential has been suggested that is based on a self-consistent
mean-field model, with the folding factor determined using the quantization
conditions of the quasibound cluster state. We have investigated the
$\alpha$-particle and heavier-cluster decays of trans-$^{100}$Sn and
trans-$^{208}$Pb nuclei, and the observed diproton emission from the proton
drip-line nucleus $^{16}$Ne, showing the overall reasonable descriptions of
cluster radioactivities with calculated half-lives agreeing well with
experimental data. We have also predicted the properties of yet unobserved
cluster decays of the exotic nuclei $^{112,114}$Ba, $^{104}$Te and $^{38}$Ti.
