In VAEs, posterior collapse occurs when the approximated posterior $q_\theta(z|x)$ becomes the standard Gaussian prior $p(z)$ after training (Lucas et al. 2019). The forward process of diffusion models transforms the data $x$ into a standard Gaussian at time step $T$, which is similar to approximating the posterior $p(z|x)$ in hierarchical VAEs (see this blog post for more details). Therefore, I am wondering whether diffusion models suffer from the issue of posterior collapse, if that makes sense at all.