<p>Probabilistic divergence measures the statistical distance between two probability distributions. Traditionally, they are used in probability theory and information theory. Nowadays, many machine learning algorithms rely on such divergences to learn models and distributions of parameters, enabling them to perform a wide range of automated tasks. This small article proposes a new family of symmetric probabilistic divergences generated using a novel functional generator. The generator uses monotonically increasing and decreasing functions to create a variety of probabilistic divergences. While it is possible to generate a variety of probabilistic divergences based on the suitable choices of functions, here the focus on six new probabilistic divergences.</p>