Diffusion probabilistic models have recently achieved remarkable success in generating high quality image and video data. In this work, we build on this class of generative models and introduce a method for lossy compression of high resolution images. The resulting codec, which we call DIffuson-based Residual Augmentation Codec (DIRAC),is the first neural codec to allow smooth traversal of the rate-distortion-perception tradeoff at test time, while obtaining competitive performance with GAN-based methods in perceptual quality. Furthermore, while sampling from diffusion probabilistic models is notoriously expensive, we show that in the compression setting the number of steps can be drastically reduced.