We derive a single-letter characterization of the fundamental distortion-rate-perception tradeoff with limited common randomness under the squared error distortion measure and the squared Wasserstein-2 perception measure. This characterization is further shown to admit an explicit evaluation in the case of Gaussian sources. In addition, we clarify two different notions of universal representation. As a byproduct, soft-covering lemmas with respect to the Wasserstein-2 distance are established.