Inverse problems, such as accelerated MRI reconstruction, are ill-posed and an infinite amount of possible and plausible solutions exist. This may not only lead to uncertainty in the reconstructed image but also in downstream tasks such as semantic segmentation. This uncertainty, however, is mostly not analyzed in the literature, even though probabilistic reconstruction models are commonly used. These models can be prone to ignore plausible but unlikely solutions like rare pathologies. Building on MRI reconstruction approaches based on diffusion models, we add guidance to the diffusion process during inference, generating two meaningfully diverse reconstructions corresponding to an upper and lower bound segmentation. The reconstruction uncertainty can then be quantified by the difference between these bounds, which we coin the 'uncertainty boundary'. We analyzed the behavior of the upper and lower bound segmentations for a wide range of acceleration factors and found the uncertainty boundary to be both more reliable and more accurate compared to repeated sampling. Code is available at https://github.com/NikolasMorshuis/SGR

翻译：逆问题（如加速磁共振成像重建）是病态的，存在无限种可能且合理的解。这不仅可能导致重建图像的不确定性，还会影响下游任务（如语义分割）的结果。然而，尽管概率重建模型已被广泛使用，这种不确定性在文献中却很少被分析。这些模型容易忽略合理但罕见的解（如罕见病理特征）。基于扩散模型的磁共振成像重建方法，我们在推理过程中向扩散过程添加引导，生成两种具有意义多样性的重建结果，分别对应分割的上界与下界。重建不确定性可通过这些边界之间的差异进行量化，我们将其称为“不确定性边界”。我们分析了上界与下界分割在多种加速因子下的表现，发现与重复采样相比，不确定性边界既更可靠又更精确。代码发布于 https://github.com/NikolasMorshuis/SGR