# Quickest Change Detection with Diffusion-Integrated Scores

arXiv: https://arxiv.org/abs/2610.12200 · HTML: https://mlsanity.com/paper/2610.12200/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 28 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 2 of 2)

- [Diffusion-Based Hypothesis Testing and Change-Point Detection](https://mlsanity.com/paper/2506.16089/) (2025)
- [Sequential Change Point Detection via Denoising Score Matching](https://mlsanity.com/paper/2501.12667/) (2025)

## Abstract (arXiv)

Classical CUSUM relies on the log-likelihood ratio of the underlying distributions, which cannot generally be computed from finite pre- and post-change samples alone. We propose diffusion-integrated score CUSUM (DI-SCUSUM), a training-free detector. We add Gaussian noise to the samples to form two smooth density estimates and calculate their Hyv"arinen scores exactly, without training a score network. For each incoming observation, we sample a diffusion time, perturb the observation, and use the importance-weighted score difference as an increment in the DI-SCUSUM recursion. Under the assumption that observations follow the fixed empirical distributions, the post-change mean increment is proportional to the Kullback-Leibler (KL) divergence from the smoothed post-change to the smoothed pre-change empirical distribution. We establish exponential false-alarm scaling and a first-order delay bound that, for a fixed threshold and increment scaling, is inversely proportional to the KL divergence. In the calibrated anisotropic Gaussian simulation, DI-SCUSUM nearly matches likelihood-ratio CUSUM and reduces the measured detection delay by about 91% relative to score-based CUSUM. On MNIST and Oxford-IIIT Pet, DI-SCUSUM also has lower empirical conditional detection delay than SCUSUM at comparable false-alarm levels.