  We generalize the family of $\alpha$-divergences using a pair of strictly
comparable weighted means. In particular, we obtain the $1$-divergence in the
limit case $\alpha\rightarrow 1$ (a generalization of the Kullback-Leibler
divergence) and the $0$-divergence in the limit case $\alpha\rightarrow 0$ (a
generalization of the reverse Kullback-Leibler divergence). We state the
condition for a pair of quasi-arithmetic means to be strictly comparable, and
report the formula for the quasi-arithmetic $\alpha$-divergences and its
subfamily of bipower homogeneous $\alpha$-divergences which belong to the
Csis\'ar's $f$-divergences. Finally, we show that these generalized
quasi-arithmetic $1$-divergences and $0$-divergences can be decomposed as the
sum of generalized cross-entropies minus entropies, and rewritten as conformal
Bregman divergences using monotone embeddings.
