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.

翻译：我们提出了一种新的生成式建模框架，该框架基于度量传输的离散时间随机控制形式。通过借鉴控制理论中的经典结果，我们将问题表述为一个线性规划，其对偶变量对应于控制问题的*最优值函数*，该函数直接编码了最优控制策略。利用该线性规划形式，我们开发了一种高效的免模拟原对偶算法，用于计算近似最优值函数及相关的*价值驱动传输*策略，该策略逼近真实的最优策略。我们表明，与基于流、扩散或薛定谔桥的其他最先进方法相比，训练良好的VDT策略具有众多有利特性：它们产生可直接快速且稳健模拟的直线传输路径，并且能够以与扩散和基于流模型完全相同的方式进行增强（例如，条件生成、无分类器引导、非配对数据到数据翻译均易于集成）。我们在一系列实验中评估了该方法，结果表明其性能强劲且具有良好的扩展潜力。