Fairness is a crucial concern for generative models, which not only reflect but can also amplify societal and cultural biases. Existing fairness notions for generative models are largely adapted from classification and focus on balancing the probability of generating samples from each sensitive group. We show that such criteria are brittle, as they can be met even when different sensitive groups are modeled with widely varying quality. To address this limitation, we introduce a new fairness definition for generative models, termed as equalized generative treatment (EGT), which requires comparable generation quality across all sensitive groups, with quality measured via a reference f-divergence. We further analyze the trade-offs induced by EGT, demonstrating that enforcing fairness constraints necessarily couples the overall model quality to that of the most challenging group to approximate. This indicates that a simple yet efficient min-max fine-tuning method should be able to balance f-divergences across sensitive groups to satisfy EGT. We validate this theoretical insight through a set of experiments on both image and text generation tasks. We demonstrate that min-max methods consistently achieve fairer outcomes compared to other approaches from the literature, while maintaining competitive overall performance for both tasks.