Training generative models with differential privacy (DP) typically involves injecting noise into gradient updates or adapting the discriminator's training procedure. We consider the \emph{slicing privacy mechanism} that injects noise into random low-dimensional projections of the private data, and provide strong privacy guarantees for it. These noisy projections are used for training generative models.To enable optimizing generative models using this DP approach, we introduce the \emph{smoothed-sliced f -divergence} and show it enjoys statistical consistency. Moreover, we present a kernel-based estimator for this divergence, circumventing the need for adversarial training. Extensive numerical experiments demonstrate that our approach can generate synthetic data of higher quality compared with baselines.