  Diffusion models are one of the most important families of deep generative
models. In this note, we derive a quantitative upper bound on the Wasserstein
distance between the data-generating distribution and the distribution learned
by a diffusion model. Unlike previous works in this field, our result does not
make assumptions on the learned score function. Moreover, our bound holds for
arbitrary data-generating distributions on bounded instance spaces, even those
without a density w.r.t. the Lebesgue measure, and the upper bound does not
suffer from exponential dependencies. Our main result builds upon the recent
work of Mbacke et al. (2023) and our proofs are elementary.
