Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the unconditioned dynamics rarely reach the terminal state. In this work, we propose a novel approach for learning diffusion bridges based on a self-consistency property of the optimal control. The resulting algorithm learns the conditioned dynamics in an iterative online manner, and exhibits strong performance in a range of empirical settings without requiring differentiation through simulated trajectories. Beyond the diffusion bridge setting, we draw connections between our self-consistency framework and recent advances in the wider stochastic optimal control literature.

翻译：模拟扩散过程在给定初始和终止状态下的条件动力学是科学领域中重要且具有挑战性的问题。这一难度在稀有事件中尤为突出，因为非条件动力学很少能达到终止状态。在本研究中，我们提出了一种基于最优控制自一致性属性的扩散桥梁学习方法。所得到的算法以迭代在线方式学习条件动力学，并在无需对模拟轨迹进行微分的情况下，在一系列实证场景中展现出强劲性能。除了扩散桥梁场景外，我们还建立了自一致性框架与更广泛随机最优控制领域最新进展之间的联系。