  The goal of text generation models is to fit the underlying real probability
distribution of text. For performance evaluation, quality and diversity metrics
are usually applied. However, it is still not clear to what extend can the
quality-diversity evaluation reflect the distribution-fitting goal. In this
paper, we try to reveal such relation in a theoretical approach. We prove that
under certain conditions, a linear combination of quality and diversity
constitutes a divergence metric between the generated distribution and the real
distribution. We also show that the commonly used BLEU/Self-BLEU metric pair
fails to match any divergence metric, thus propose CR/NRR as a substitute for
quality/diversity metric pair.
