Achieving a balance between image quality (precision) and diversity (recall)
is a significant challenge in the domain of generative models. Current
state-of-the-art models primarily rely on optimizing heuristics, such as the
Fr\'echet Inception Distance. While recent developments have introduced
principled methods for evaluating precision and recall, they have yet to be
successfully integrated into the training of generative models. Our main
contribution is a novel training method for generative models, such as
Generative Adversarial Networks and Normalizing Flows, which explicitly
optimizes a user-defined trade-off between precision and recall. More
precisely, we show that achieving a specified precision-recall trade-off
corresponds to minimizing a unique f-divergence from a family we call the
\mbox{\em PR-divergences}. Conversely, any f-divergence can be written as a
linear combination of PR-divergences and corresponds to a weighted
precision-recall trade-off. Through comprehensive evaluations, we show that our
approach improves the performance of existing state-of-the-art models like
BigGAN in terms of either precision or recall when tested on datasets such as
ImageNet