New advancements for the detection of synthetic images are critical for fighting disinformation, as the capabilities of generative AI models continuously evolve and can lead to hyper-realistic synthetic imagery at unprecedented scale and speed. In this paper, we focus on the challenge of generalizing across different concept classes, e.g., when training a detector on human faces and testing on synthetic animal images -- highlighting the ineffectiveness of existing approaches that randomly sample generated images to train their models. By contrast, we propose an approach based on the premise that the robustness of the detector can be enhanced by training it on realistic synthetic images that are selected based on their quality scores according to a probabilistic quality estimation model. We demonstrate the effectiveness of the proposed approach by conducting experiments with generated images from two seminal architectures, StyleGAN2 and Latent Diffusion, and using three different concepts for each, so as to measure the cross-concept generalization ability. Our results show that our quality-based sampling method leads to higher detection performance for nearly all concepts, improving the overall effectiveness of the synthetic image detectors.