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As we expect to see a rapid integration of generative models in our day to day lives, the development of rigorous methods of evaluation and analysis for generative models has never been more pressing. Multiple works have highlighted the shortcomings of widely used metrics and exposed how they fail to behave as expected in some settings. So far, the response has been to use a variety of metrics that target different desirable and interpretable properties such as fidelity, diversity, and authenticity, to obtain a clearer picture of a generative model’s capabilities. These methods mainly focus on ordinal data and they all suffer from the same unavoidable issues stemming from estimating quantities of high-dimensional data from a limited number of samples. We propose to take an alternative approach and to return to the synthetic data setting where the ground truth is explicit and known. We focus on nominal categorical data and introduce an evaluation method that can scale to the high-dimensional settings often encountered in practice. Our method involves successively binning the large space to obtain smaller probability spaces and coarser distributions where meaningful statistical estimates can be obtained. This allows us to provide probabilistic guarantees and sample complexities and we illustrate how our method can be applied to distinguish between the capabilities of several state-of-the-art categorical models.