Unsupervised Detection of Distribution Shift in Inverse Problems using Diffusion Models
Journal:
arXiv
Published Date:
May 16, 2025
Abstract
Diffusion models are widely used as priors in imaging inverse problems.
However, their performance often degrades under distribution shifts between the
training and test-time images. Existing methods for identifying and quantifying
distribution shifts typically require access to clean test images, which are
almost never available while solving inverse problems (at test time). We
propose a fully unsupervised metric for estimating distribution shifts using
only indirect (corrupted) measurements and score functions from diffusion
models trained on different datasets. We theoretically show that this metric
estimates the KL divergence between the training and test image distributions.
Empirically, we show that our score-based metric, using only corrupted
measurements, closely approximates the KL divergence computed from clean
images. Motivated by this result, we show that aligning the out-of-distribution
score with the in-distribution score -- using only corrupted measurements --
reduces the KL divergence and leads to improved reconstruction quality across
multiple inverse problems.
