Generative Modeling with Phase Stochastic Bridge

We introduce a novel generative modeling framework grounded in phase space dynamics, taking inspiration from the principles underlying Critically damped Langevin Dynamics and Bridge Matching. Leveraging insights from Stochastic Optimal Control, we construct a more favorable path measure in the phase space that is highly advantageous for efficient sampling. A distinctive feature of our approach is the early-stage data prediction capability within the context of propagating generative Ordinary Differential Equations or Stochastic Differential Equations. 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 quickly converging to realistic data samples. Our model yields comparable results in image generation and notably outperforms baseline methods, particularly when faced with a limited Number of Function Evaluations. Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential in the realm of generative modeling. Code is available at https://github.com/apple/ml-agm .