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Poster
Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance
Dohyun Kwon · Ying Fan · Kangwook Lee

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #415
in Poster Session 4 »

Score-based generative models are shown to achieve remarkable empirical performances in various applications such as image generation and audio synthesis. However, a theoretical understanding of score-based diffusion models is still incomplete. Recently, Song et al. showed that the training objective of score-based generative models is equivalent to minimizing the Kullback-Leibler divergence of the generated distribution from the data distribution. In this work, we show that score-based models also minimize the Wasserstein distance between them. Specifically, we prove that the Wasserstein distance is upper bounded by the square root of the objective function up to multiplicative constants and a fixed constant offset. Our proof is based on a novel application of the theory of optimal transport, which can be of independent interest to the society. Our numerical experiments support our findings. By analyzing our upper bounds, we provide a few techniques to obtain tighter upper bounds.

Keywords: optimal transport · score-based generative models · wasserstein distance
[ Paper]  [ Poster]  [ OpenReview] 

Author Information

Dohyun Kwon (University of Wisconsin - Madison)
Ying Fan (University of Wisconsin-Madison)
Kangwook Lee (UW Madison, Krafton)

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