  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.
