This paper introduces a novel generative modeling framework grounded in phase space dynamics, taking inspiration from the principles underlying Critically Damped Langevin Dynamics (CLD). Leveraging insights from stochastic optimal control, we construct a favorable path measure in the phase space that proves highly advantageous for generative sampling. A distinctive feature of our approach is the early-stage data prediction capability within the context of propagating generating Ordinary Differential Equations (ODEs) or Stochastic Differential Equations (SDEs) processes. This early prediction, enabled by the model’s unique structural characteristics, sets the stage for more efficient data generation, leveraging additional velocity information along the trajectory. This innovation has spurred the exploration of a novel avenue for mitigating sampling complexity by transitioning directly from noisy data to authentic images. Our model yields comparable results in image generation and notably outperforms baseline methods, particularly when faced with a limited Number of Function Evaluations (NFE). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential in the realm of generative modeling.
