PQMass: Probabilistic Assessment of the Quality of Generative Models using Probability Mass Estimation

We propose a comprehensive sample-based method for assessing the quality of generative models. The proposed approach enables the estimation of the probability that two sets of samples are drawn from the same distribution, providing a statistically rigorous method for assessing the performance of a single generative model or the comparison of multiple competing models trained on the same dataset. This comparison can be conducted by dividing the space into non-overlapping regions and comparing the number of data samples in each region. The method only requires samples from the generative model and the test data. It is capable of functioning directly on high-dimensional data, obviating the need for dimensionality reduction. Significantly, the proposed method does not depend on assumptions regarding the density of the true distribution, and it does not rely on training or fitting any auxiliary models. Instead, it focuses on approximating the integral of the density (probability mass) across various sub-regions within the data space.