Diffusion models have achieved remarkable success in generating high-quality and diverse outputs, supported by stable and scalable training procedures. However, when applied to real-world scenarios, they continue to exhibit key limitations. In this talk, I will examine several of these fundamental challenges, including slow sampling, inadequate modeling of distributional tails, and inefficiencies in training. I will also present recent advances aimed at mitigating these issues, focusing on techniques such as accelerated sampling via trajectory and distribution matching objectives, as well as improved diffusion processes designed specifically for video generation. The talk will conclude with a discussion of emerging requirements for generative models, particularly their ability to capture rare events and heavy-tailed data distributions.