The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our model can determine the initial conditions necessary to reach a desired terminal distribution by adapting an existing score function. We demonstrate the theoretical guarantees of the model, the benefits of using Lipschitz networks for score matching, and its potential applications in various areas such as diffusion inversion, conditional diffusion, and uncertainty quantification. Our work represents a contribution to the field of score-based generative learning and offers a promising direction for solving real-world problems.

翻译：所提出的基于BSDE的扩散模型代表了扩散建模的一种新方法，它扩展了随机微分方程（SDEs）在机器学习中的应用。与传统的基于SDE的扩散模型不同，我们的模型通过适配现有的得分函数，能够确定达到期望终端分布所需的初始条件。我们展示了该模型的理论保证、使用Lipschitz网络进行得分匹配的优势，及其在扩散反演、条件扩散和不确定性量化等多个领域的潜在应用。我们的工作为基于得分的生成学习领域做出了贡献，并为解决实际问题提供了一条有前景的方向。