This paper studies the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. The perception measure is based on a divergence between the distributions of the source and reconstruction sequences \emph{conditioned} on the encoder output, first proposed by Mentzer et al. We consider the case when there is no shared randomness between the encoder and the decoder. For the case of discrete memoryless sources we derive a single-letter characterization of the RDP function, in contrast to the marginal-distribution metric case (introduced by Blau and Michaeli), whose RDP characterization remains open when there is no shared randomness. The achievability scheme is based on lossy source coding with a posterior reference map. For the case of continuous valued sources under squared error distortion measure and squared quadratic Wasserstein perception measure we also derive a single-letter characterization and show that a noise-adding mechanism at the decoder suffices to achieve the optimal representation. Interestingly, the RDP function characterized for the case of zero perception loss coincides with that of the marginal metric and further zero perception loss can be achieved with a $3$-dB penalty in minimum distortion. Finally we specialize to the case of Gaussian sources, and derive the RDP function for Gaussian vector case and propose a waterfilling like solution. We also partially characterize the RDP function for a mixture of Gaussian vector sources.