In probability theory, an f {\displaystyle f} -divergence is a certain type of function D f ( P ‖ Q ) {\displaystyle D_{f}(P\|Q)} that measures the difference between two probability distributions P {\displaystyle P} and Q {\displaystyle Q} . Many common divergences, such as KL-divergence, Hellinger distance, and total variation distance, are special cases of f {\displaystyle f} -divergence.