When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated probabilities are embedded in the posterior distribution. However, when confronted with data of high dimensionality (such as images), visualizing this distribution becomes a formidable challenge, necessitating the application of effective summarization techniques before user examination. In this work, we introduce a new approach for visualizing posteriors across multiple levels of granularity using tree-valued predictions. Our method predicts a tree-valued hierarchical summarization of the posterior distribution for any input measurement, in a single forward pass of a neural network. We showcase the efficacy of our approach across diverse datasets and image restoration challenges, highlighting its prowess in uncertainty quantification and visualization. Our findings reveal that our method performs comparably to a baseline that hierarchically clusters samples from a diffusion-based posterior sampler, yet achieves this with orders of magnitude greater speed.

翻译：在求解不适定逆问题时，研究者通常期望探索潜在解的空间，而非仅获得单一可行的重建结果。关于这些可行解及其对应概率的重要信息蕴含于后验分布之中。然而，当面对高维数据（如图像）时，可视化该分布成为一项艰巨挑战，必须在用户检视前采用有效的摘要技术。本研究提出一种利用树值预测实现多粒度后验可视化的新方法。我们的方法通过神经网络单次前向传播，即可为任意输入测量值预测后验分布的树值分层摘要。我们在多种数据集和图像复原任务中验证了该方法的有效性，突显其在不确定性量化与可视化方面的优势。实验结果表明，本方法性能与基于扩散后验采样器进行分层聚类的基线方法相当，但计算速度提升数个数量级。