We consider the problem of simulating diffusion bridges, i.e. diffusion processes that are conditioned to initialize and terminate at two given states. Diffusion bridge simulation has applications in diverse scientific fields and plays a crucial role for statistical inference of discretely-observed diffusions. This is known to be a challenging problem that has received much attention in the last two decades. In this work, we first show that the time-reversed diffusion bridge process can be simulated if one can time-reverse the unconditioned diffusion process. We introduce a variational formulation to learn this time-reversal that relies on a score matching method to circumvent intractability. We then consider another iteration of our proposed methodology to approximate the Doob's $h$-transform defining the diffusion bridge process. As our approach is generally applicable under mild assumptions on the underlying diffusion process, it can easily be used to improve the proposal bridge process within existing methods and frameworks. We discuss algorithmic considerations and extensions, and present some numerical results.

本文提出了一种基于反向时间表示的扩散桥模拟方法，通过变分公式学习时空逆转实现扩散桥的模拟，并通过评分匹配方法克服其不可计算性，提出了一种近似 Doob's h-变换法的方法，实验结果表明了此方法的有效性。

使用得分匹配模拟扩散跃点