  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.
