In recent years, diffusion models (DMs) have become a popular method for generating synthetic data. By achieving samples of higher quality, they quickly became superior to generative adversarial networks (GANs) and the current state-of-the-art method in generative modeling. However, their potential has not yet been exploited in radar, where the lack of available training data is a long-standing problem. In this work, a specific type of DMs, namely denoising diffusion probabilistic model (DDPM) is adapted to the SAR domain. We investigate the network choice and specific diffusion parameters for conditional and unconditional SAR image generation. In our experiments, we show that DDPM qualitatively and quantitatively outperforms state-of-the-art GAN-based methods for SAR image generation. Finally, we show that DDPM profits from pretraining on largescale clutter data, generating SAR images of even higher quality.