Building generative surrogates for expensive event generation and simulation tasks is a key step in enabling the physics program of the high-luminosity LHC (HL-LHC) and future collider studies [1-3]. As experiments in high energy physics push the boundaries of luminosity resulting in ever increasing event rates, the computational demand of high-precision Monte Carlo (MC) simulations is growing to the point where it will soon surpass available computational resources [4]. Generative models offer a promising solution to this challenge, potentially reducing the immense computational load required for these simulations. This has led to substantial research into the development of machine-learning architectures tailored for more efficient and accurate detector simulation [5, 6]. Examples include generative adversarial networks (GANs) [7-18], variational autoencoders (V AEs) and their variants [18-24], normalizing flows and various types of diffusion models [23, 25-45], as well as generative pre-trained transformer (GPT) style models [46]. The combination of a diffusion model with a transformer architecture, known as diffusion transformers [47, 48], has been used in high-energy physics for jet generation [45, 49-52]. The majority of these studies have focused on simulating electromagnetic showers, for a recent review see [53].