Strong generative models can accurately learn wireless channel distributions, enabling data-driven channel emulation when mathematical descriptions are intractable. Moreover, differentiable channel models facilitate gradient-based training of neural encoders within end-to-end (E2E) communication frameworks. While prior studies have primarily relied on generative adversarial networks (GANs) for this purpose, this paper investigates diffusion models (DMs) as an alternative approach for channel approximation. We develop a DM-based channel modeling framework that integrates efficiently into E2E coded-modulation systems and propose a stable pre-training algorithm for faster and more reliable convergence. Through controlled simulations across a range of canonical channel models, we show that DMs achieve near-optimal symbol error rates (SERs) and mode coverage. In particular, the advantage of DMs in mode coverage becomes evident for complex channel models with temporal correlation and strong nonlinearity, whereas both DMs and GANs accurately capture the distributions of relatively simple channel models. We further analyze the trade-off between mode coverage and sampling efficiency using skipped sampling and the denoising diffusion implicit model, quantified via sliced Wasserstein distance and E2E SER. The results demonstrate that appropriate parameter choices can substantially reduce sampling time with minimal degradation in generative performance. Overall, this study establishes a baseline and empirical foundation for diffusion-based channel generation, providing insights into their scalability and potential for realistic communication environments.