Image codecs are typically optimized to trade-off bitrate vs. distortion metrics. At low bitrates, this leads to compression artefacts which are easily perceptible, even when training with perceptual distortion metrics or adversarial losses. To improve image quality, and to make it less dependent on the bitrate, we propose to leverage diffusion models as a decoder module, which rely on an iterative decoding process instead of feed-forward decoders trained using MSE or LPIPS distortions used in most neural codecs. In addition to conditioning the model on a vector-quantized image representation, we also condition on a global textual image description to provide additional context. We dub our model PerCo for ''perceptual compression'', and compare it to state-of-the-art codecs at bitrates from 0.1 down to 0.003 bits per pixel (bpp). The latter rate is an order of magnitude smaller than those considered in most prior work. At this bitrate a 512x768 Kodak image is encoded in just 148 bytes. Despite this ultra-low bitrate, our approach maintains the ability to reconstruct realistic images. We find that our model leads to reconstructions with state-of-the-art visual quality as measured by FID and KID, and that the visual quality is less dependent on the bitrate than previous methods. Image codecs are typically optimized to trade-off bitrate vs. distortion metrics. At low bitrates, this leads to compression artefacts which are easily perceptible, even when training with perceptual or adversarial losses. To improve image quality, and to make it less dependent on the bitrate, we propose to decode with iterative diffusion models, instead of feed-forward decoders trained using MSE or LPIPS distortions used in most neural codecs. In addition to conditioning the model on a vector-quantized image representation, we also condition on a global textual image description to provide additional context. We dub our model PerCo for ''perceptual compression'', and compare it to state-of-the-art codecs at rates from 0.1 down to 0.003 bits per pixel. The latter rate is an order of magnitude smaller than those considered in most prior work. At this bitrate a 512x768 Kodak image is encoded in less than 153 bytes. Despite this ultra-low bitrate, our approach maintains the ability to reconstruct realistic images. We find that our model leads to reconstructions with state-of-the-art visual quality as measured by FID and KID, and that the visual quality is less dependent on the bitrate than previous methods.