Score-based Generative Models (SGMs) have demonstrated impressive performance in data generation, as highlighted in recent research. Building on this foundation, Critically-damped Langevin Diffusions (CLDs) have been introduced, drawing inspiration from Hamiltonian dynamics. These CLDs enhance traditional diffusion processes by coupling the data with auxiliary variables, a methodological innovation that distinguishes them from earlier approaches. The incorporation of auxiliary variables allows CLDs to exhibit strong theoretical guarantees, ensuring robust convergence properties. Moreover, the versatility of CLDs is reflected in their broad range of applications across various domains. This advancement represents a significant step forward in the development of generative modeling techniques. The research underscores the potential of combining physical dynamics principles with machine learning to improve generative performance.