CaloDREAM is a novel framework for detector response simulation using Conditional Flow Matching (CFM) combined with transformer elements. The authors address the challenge of simulating high-dimensional phase spaces in calorimeter showers, which are crucial for LHC data analysis. They use an autoregressive transformer to simulate layer energies and a vision transformer for high-dimensional voxel distributions. Dimension reduction via latent diffusion allows for more efficient training and faster evaluation with bespoke solvers. The framework, CaloDREAM, is evaluated on datasets 2 and 3 of the CaloChallenge, demonstrating high-fidelity calorimeter shower simulations. The study highlights the effectiveness of the proposed approach in handling sparse and high-dimensional data, with potential applications in LHC simulations and event generation.CaloDREAM is a novel framework for detector response simulation using Conditional Flow Matching (CFM) combined with transformer elements. The authors address the challenge of simulating high-dimensional phase spaces in calorimeter showers, which are crucial for LHC data analysis. They use an autoregressive transformer to simulate layer energies and a vision transformer for high-dimensional voxel distributions. Dimension reduction via latent diffusion allows for more efficient training and faster evaluation with bespoke solvers. The framework, CaloDREAM, is evaluated on datasets 2 and 3 of the CaloChallenge, demonstrating high-fidelity calorimeter shower simulations. The study highlights the effectiveness of the proposed approach in handling sparse and high-dimensional data, with potential applications in LHC simulations and event generation.