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The machine learning community has mainly relied on real data to benchmark algorithms as it provides compelling evidence of model applicability. Evaluation on synthetic datasets can be a powerful tool to provide a better understanding of a model's strengths, weaknesses, and overall capabilities. Gaining these insights can be particularly important for generative modeling as the target quantity is completely unknown. Multiple issues related to the evaluation of generative models have been reported in the literature. We argue those problems can be avoided by an evaluation based on ground truth. General criticisms of synthetic experiments are that they are too simplified and not representative of practical scenarios. As such, our experimental setting is tailored to a realistic generative task. We focus on categorical data and introduce an appropriately scalable evaluation method. Our method involves tasking a generative model to learn a distribution in a high-dimensional setting. We then successively bin the large space to obtain smaller probability spaces where meaningful statistical tests can be applied. We consider increasingly large probability spaces, which correspond to increasingly difficult modeling tasks and compare the generative models based on the highest task difficulty they can reach before being detected as being too far from the ground truth. We validate our evaluation procedure with synthetic experiments on both synthetic generative models and current state-of-the-art categorical generative models.