ICLR 2025

Published as a conference paper at ICLR 2025
PROGRESSIVE COMPRESSION WITH
UNIVERSALLY QUANTIZED DIFFUSION MODELS
Yibo Yang∗
Justus C. Will∗
Stephan Mandt
Department of Computer Science
University of California, Irvine
{yibo.yang, jcwill, mandt}@uci.edu
ABSTRACT
Diffusion probabilistic models have achieved mainstream success in many gen-
erative modeling tasks, from image generation to inverse problem solving. A
distinct feature of these models is that they correspond to deep hierarchical latent
variable models optimizing a variational evidence lower bound (ELBO) on the
data likelihood. Drawing on a basic connection between likelihood modeling and
compression, we explore the potential of diffusion models for progressive coding,
resulting in a sequence of bits that can be incrementally transmitted and decoded
with progressively improving reconstruction quality. Unlike prior work based on
Gaussian diffusion or conditional diffusion models, we propose a new form of
diffusion model with uniform noise in the forward process, whose negative ELBO
corresponds to the end-to-end compression cost using universal quantization. We
obtain promising first results on image compression, achieving competitive rate-
distortion and rate-realism results on a wide range of bit-rates with a single model,
bringing neural codecs a step closer to practical deployment. Our code can be
found at https://github.com/mandt-lab/uqdm.
1
INTRODUCTION
A diffusion probabilistic model can be equivalently viewed as a deep latent-variable model (Sohl-
Dickstein et al., 2015; Ho et al., 2020; Kingma et al., 2021), a cascade of denoising autoencoders that
perform score matching at different noise levels (Vincent, 2011; Song & Ermon, 2019), or a neural
SDE (Song et al., 2021b). Here we take the latent-variable model view and explore the potential of
diffusion models for communicating information. Given the strong performance of these models on
likelihood estimation (Kingma et al., 2021; Nichol & Dhariwal, 202...