This paper presents a novel generative modeling framework based on phase space dynamics, drawing inspiration from the principles underlying critically damped Langevin dynamics (CLD). Leveraging insights from stochastic optimal control, we construct a favorable path measure in phase space that is highly advantageous for generative sampling. A distinctive feature of our approach is the ability to predict data at early stages within the context of the propagation of ordinary differential equation (ODE) or stochastic differential equation (SDE) generation processes. This early prediction, enabled by the model's unique structural features, sets the stage for more efficient data generation, taking advantage of additional velocity information along the trajectory. This innovation has stimulated the exploration of a new avenue to mitigate sampling complexity by directly transitioning noisy data to authentic images. Our model produces comparable results in image generation and significantly outperforms baseline methods, particularly when faced with a limited number of feature evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential in the realm of generative modeling.
