  Diffusion models have emerged as a popular family of deep generative models
(DGMs). In the literature, it has been claimed that one class of diffusion
models -- denoising diffusion probabilistic models (DDPMs) -- demonstrate
superior image synthesis performance as compared to generative adversarial
networks (GANs). To date, these claims have been evaluated using either
ensemble-based methods designed for natural images, or conventional measures of
image quality such as structural similarity. However, there remains an
important need to understand the extent to which DDPMs can reliably learn
medical imaging domain-relevant information, which is referred to as `spatial
context' in this work. To address this, a systematic assessment of the ability
of DDPMs to learn spatial context relevant to medical imaging applications is
reported for the first time. A key aspect of the studies is the use of
stochastic context models (SCMs) to produce training data. In this way, the
ability of the DDPMs to reliably reproduce spatial context can be
quantitatively assessed by use of post-hoc image analyses. Error-rates in
DDPM-generated ensembles are reported, and compared to those corresponding to a
modern GAN. The studies reveal new and important insights regarding the
capacity of DDPMs to learn spatial context. Notably, the results demonstrate
that DDPMs hold significant capacity for generating contextually correct images
that are `interpolated' between training samples, which may benefit
data-augmentation tasks in ways that GANs cannot.
