  We consider a novel lossy compression approach based on unconditional
diffusion generative models, which we call DiffC. Unlike modern compression
schemes which rely on transform coding and quantization to restrict the
transmitted information, DiffC relies on the efficient communication of pixels
corrupted by Gaussian noise. We implement a proof of concept and find that it
works surprisingly well despite the lack of an encoder transform, outperforming
the state-of-the-art generative compression method HiFiC on ImageNet 64x64.
DiffC only uses a single model to encode and denoise corrupted pixels at
arbitrary bitrates. The approach further provides support for progressive
coding, that is, decoding from partial bit streams. We perform a
rate-distortion analysis to gain a deeper understanding of its performance,
providing analytical results for multivariate Gaussian data as well as
theoretic bounds for general distributions. Furthermore, we prove that a
flow-based reconstruction achieves a 3 dB gain over ancestral sampling at high
bitrates.
