发表机构
Georgia Institute of Technology（佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出联合扭转流，一种增强流匹配方法，通过耦合观测一致性来改善贝叶斯逆问题中的后验采样，保留多模态变异性，并在低维、图像恢复和地震反演中验证有效性。
AI 中文摘要
在贝叶斯逆问题中，后验采样需要生成与给定观测一致且能捕捉合理解范围的样本。直接条件生成模型引入潜在噪声来建模这种模糊性，但配对逆问题训练仍可能鼓励从观测到目标的近乎确定性映射。因此，生成的样本可能满足观测一致性，但低估了后验变异性，尤其是在后验为多模态时，导致覆盖不足、模态失真或不同可行解之间的人为转换。我们提出联合扭转流（joint twist-flow），一种增强的流匹配公式，学习从增强源状态$(z_x, y)$到增强终态$(x, z_y)$的连续传输。这里$x$是目标变量，$y$是观测，$z_x$是用于后验采样的高斯参考坐标，$z_y$是与观测分支相关的高斯似然侧坐标。在高斯观测模型下，$z_y$由与观测兼容性相关的归一化观测残差驱动。其作用不是替代$x$中的不确定性，而是将生成的$x$样本与观测一致性耦合，帮助减少似然不一致的变化，同时保留弱约束方向上的变异性。我们在具有参考后验样本的低维逆问题上验证了该方法，联合扭转流比直接条件流基线更好地保留了多模态后验支持。我们进一步在图像恢复和地震地下速度模型反演上评估了该方法，显示在保持观测一致性的同时增加了后验变异性。
英文摘要
In Bayesian inverse problems, posterior sampling requires generating samples that are consistent with given observations while capturing the range of plausible solutions. Direct conditional generative models introduce latent noise to model this ambiguity, but paired inverse-problem training can still encourage an almost deterministic map from the observation to the target. As a result, generated samples may be observation-consistent while under-representing posterior variability, especially when the posterior is multimodal, leading to undercoverage, mode distortion, or artificial transitions between distinct feasible solutions. We propose joint twist-flow, an augmented flow-matching formulation that learns a continuous transport from the augmented source state $(z_x, y)$ to the augmented terminal state $(x, z_y)$. Here x is the target variable, $y$ is the observation, $z_x$ is the Gaussian reference coordinate for posterior sampling, and $z_y$ is a Gaussian likelihood-side coordinate associated with the observation branch. Under a Gaussian observation model, $z_y$ is motivated by the normalized observation residual associated with observation compatibility. Its role is not to replace uncertainty in $x$, but to couple generated samples of x to observation consistency, helping reduce likelihood-inconsistent variation while preserving variability in weakly constrained directions. We validate the method on low-dimensional inverse problems with reference posterior samples, where joint twist-flow better preserves multimodal posterior support than a direct conditional-flow baseline. We further evaluate the method on image restoration and seismic subsurface velocity-model inversion, showing increased posterior variability while maintaining observation consistency.
