Title: SPREAD  DIVERGENCE. Abstract: For distributions $p$ and $q$ with different supports, the divergence $\div{p}{q}$ may not exist. We define a spread divergence $\sdiv{p}{q}$ on modified $p$ and $q$ and describe sufficient conditions for the existence of such a divergence. We demonstrate how to maximize the discriminatory power of a given divergence by parameterizing and learning the spread. We also give examples of using a spread divergence to train and improve implicit generative models, including linear models (Independent Components Analysis) and non-linear models (Deep Generative Networks).