  In privacy-preserving machine learning, differentially private stochastic
gradient descent (DP-SGD) performs worse than SGD due to per-sample gradient
clipping and noise addition. A recent focus in private learning research is
improving the performance of DP-SGD on private data by incorporating priors
that are learned on real-world public data. In this work, we explore how we can
improve the privacy-utility tradeoff of DP-SGD by learning priors from images
generated by random processes and transferring these priors to private data. We
propose DP-RandP, a three-phase approach. We attain new state-of-the-art
accuracy when training from scratch on CIFAR10, CIFAR100, MedMNIST and ImageNet
for a range of privacy budgets $\varepsilon \in [1, 8]$. In particular, we
improve the previous best reported accuracy on CIFAR10 from $60.6 \%$ to $72.3
\%$ for $\varepsilon=1$.
