Generative Modeling by Value-Driven Transport
This work provides a new paradigm for generative modeling that combines the benefits of optimal transport and control theory, offering a simulation-free algorithm with favorable properties like straight paths and easy integration of conditional generation.
The paper introduces Value-Driven Transport (VDT), a new generative modeling framework based on a discrete-time stochastic control formulation of measure transport. VDT achieves straight transport paths for fast and robust simulation, and demonstrates strong performance across various experiments, with potential for scalability.
We propose a new framework for generative modeling based on a discrete-time stochastic control formulation of measure transport. Adapting classic results from control theory, we formulate our problem as a linear program whose dual variables correspond to the \emph{optimal value function} of the control problem, which directly encodes the optimal control policy. Exploiting this LP formulation, we develop an efficient simulation-free primal-dual algorithm for computing approximately optimal value functions and the associated \emph{value-driven transport} (VDT) policies which approximate the true optimal policy. We show that well-trained VDT policies enjoy numerous favorable properties in comparison with other state-of-the-art methods based on flows, diffusions, or Schrödinger bridges: they lead to straight transport paths which can be simulated quickly and robustly, and can be enhanced in all the same ways as diffusion and flow-based models (e.g., conditional generation, classifier-free guidance, unpaired data-to-data translation are all easy to incorporate). We evaluate our methodology in a range of experiments, with results that indicate strong performance and good potential for scalability.