While the success of deep learning relies on large amounts of training datasets, data is often limited in privacy-sensitive domains. To address this challenge, generative model learning with differential privacy has emerged as a solution to train private generative models for desensitized data generation. However, the quality of the images generated by existing methods is limited due to the complexity of modeling data distribution. We build on the success of diffusion models and introduce DP-SAD, which trains a private diffusion model by a stochastic adversarial distillation method. Specifically, we first train a diffusion model as a teacher and then train a student by distillation, in which we achieve differential privacy by adding noise to the gradients from other models to the student. For better generation quality, we introduce a discriminator to distinguish whether an image is from the teacher or the student, which forms the adversarial training. Extensive experiments and analysis clearly demonstrate the effectiveness of our proposed method.