Title: Differentially Private Diffusion Models. Abstract: While modern machine learning models rely on increasingly large training datasets, data is often limited in privacy-sensitive domains. Generative models trained with differential privacy (DP) on sensitive data can sidestep this challenge, providing access to synthetic data instead. However, training DP generative models is highly challenging due to the noise injected into training to enforce DP. We propose to leverage diffusion models (DMs), an emerging class of deep generative models, and introduce Differentially Private Diffusion Models (DPDMs), which enforce privacy using differentially private stochastic gradient descent (DP-SGD). We motivate why DP-SGD is well suited for training DPDMs, and thoroughly investigate the DM parameterization and the sampling algorithm, which turn out to be crucial ingredients in DPDMs. Furthermore, we propose noise multiplicity, a simple yet powerful modification of the DM training objective tailored to the DP setting to boost performance. We validate our novel DPDMs on widely-used image generation benchmarks and achieve state-of-the-art (SOTA) performance by large margins. For example, on MNIST we improve the SOTA FID from 48.4 to 5.01 and downstream classification accuracy from 83.2% to 98.1% for the privacy setting DP-$(\varepsilon=10, \delta=10^{-5})$. Moreover, on standard benchmarks, classifiers trained on DPDM-generated synthetic data perform on par with task-specific DP-SGD-trained classifiers, which has not been demonstrated before for DP generative models.