  Strong generative models can accurately learn channel distributions. This
could save recurring costs for physical measurements of the channel. Moreover,
the resulting differentiable channel model supports training neural encoders by
enabling gradient-based optimization. The initial approach in the literature
draws upon the modern advancements in image generation, utilizing generative
adversarial networks (GANs) or their enhanced variants to generate channel
distributions. In this paper, we address this channel approximation challenge
with diffusion models (DMs), which have demonstrated high sample quality and
mode coverage in image generation. In addition to testing the generative
performance of the channel distributions, we use an end-to-end (E2E)
coded-modulation framework underpinned by DMs and propose an efficient training
algorithm. Our simulations with various channel models show that a DM can
accurately learn channel distributions, enabling an E2E framework to achieve
near-optimal symbol error rates (SERs). Furthermore, we examine the trade-off
between mode coverage and sampling speed through skipped sampling using sliced
Wasserstein distance (SWD) and the E2E SER. We investigate the effect of noise
scheduling on this trade-off, demonstrating that with an appropriate choice of
parameters and techniques, sampling time can be significantly reduced with a
minor increase in SWD and SER. Finally, we show that the DM can generate a
correlated fading channel, whereas a strong GAN variant fails to learn the
covariance. This paper highlights the potential benefits of using DMs for
learning channel distributions, which could be further investigated for various
channels and advanced techniques of DMs.
