Comment by stefanbaumann

Both Latent Consistency Models and Adversarial Diffusion Distillation (the method behind SDXL Turbo) are methods that do not depend on any specific properties of the backbone. So, as Hourglass Diffusion Transformers are just a new kind of backbone that can be used just like the Diffusion U-Nets in Stable Diffusion (XL), these methods should also be applicable to it.