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.

该论文提出了基于BSDE的扩散模型，采用适应现有评分函数的方法，确定在达到所需终端分布所需的初始条件。研究表明，采用Lipschitz网络进行评分匹配具有优势，该方法具有应用于不同领域（如扩散反演、条件扩散和不确定性量化）的潜力。该工作对得分为基础的生成学习领域做出了贡献，并为解决实际问题提供了一个有前途的方向。

逆向随机微分方程的基于得分的生成建模：反演和生成