发表机构
University of Tennessee, Chattanooga（田纳西大学查塔努加分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于倒向随机微分方程的终端条件反演方法，将预训练扩散先验与物理约束结合，实现严格可行性保证，并在稀疏视图CT重建中验证了改进效果。
AI 中文摘要
预训练的基于分数的扩散模型提供了强大的无条件先验，但在逆问题中强制测量或物理一致性通常通过启发式引导、间歇投影或任务特定的条件训练来处理，在推理结束时可行性保证有限。我们提出了针对基于分数的SDE先验的终端条件反演方法。给定一个冻结的Score-SDE先验和一个任务定义的终端可行性规范，我们构造一个关联的倒向随机微分方程，其适应解定义了一个从终端要求到选定噪声水平下先验状态的原则性逆映射。在标准正则性条件下，我们建立了适应解的存在性和唯一性，并通过构造获得终端一致性。我们进一步开发了一个实用的神经BSDE求解器，该求解器将任意预训练的扩散先验与域约束组合，而不修改分数定义的系数，产生一个锚定先验状态，从而能够进行邻域采样以进行不确定性表征。在玩具数据集上的实验验证了稳定的终端条件反演和分布一致的邻域采样。作为真实世界案例研究，我们将该框架应用于稀疏视图CT重建，并在规定的终端规范下满足严格测量可行性的同时，相较于代表性的无训练基线实现了改进的重建质量。项目可在以下网址获取：\href{this https URL}{this https URL}
英文摘要
Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is often handled by heuristic guidance, intermittent projections, or task-specific conditional training, with limited guarantees of feasibility at the end of inference. We propose terminal-conditioned inversion for score-based SDE priors. Given a frozen Score-SDE prior and a task-defined terminal feasibility specification, we construct an associated backward stochastic differential equation whose adapted solution defines a principled inverse map from the terminal requirement to a prior state at a chosen noise level. Under standard regularity conditions, we establish existence and uniqueness of the adapted solution and obtain terminal consistency by construction. We further develop a practical neural BSDE solver that composes arbitrary pretrained diffusion priors with domain constraints without modifying the score-defined coefficients, producing an anchored prior state that enables neighborhood sampling for uncertainty characterization. Experiments on toy datasets validate stable terminal-conditioned inversion and distributionally consistent neighborhood sampling. As a real-world case study, we apply the framework to sparse-view CT reconstruction and achieve improved reconstruction quality over representative training-free baselines while satisfying strict measurement feasibility under the prescribed terminal specification. Project is available in: \href{https://laplacelab.github.io/BSDEDiffusion/}{https://laplace.center/icmlbsdeI/}
CommentsAccepted as ICML paper
Journal refZihao Wang, Backward SDEs-based Diffusion for Physics-Constrained Generation, Forty-third International Conference on Machine Learning 2026
