# Diffusion-Based Hypothesis Testing and Change-Point Detection

arXiv: https://arxiv.org/abs/2506.16089 · HTML: https://mlsanity.com/paper/2506.16089/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 35 references that are in the map.
- First posted on arXiv 19 Jun 2025.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Minimum Stein Discrepancy Estimators](https://mlsanity.com/paper/1906.08283/) (2019)
- [Gaussian-Bernoulli RBMs Without Tears](https://mlsanity.com/paper/2210.10318/) (2022)
- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)
- [Quickest Change Detection for Unnormalized Statistical Models](https://mlsanity.com/paper/2302.00250/) (2023)
- [Score-Based Metropolis-Hastings Algorithms](https://mlsanity.com/paper/2501.00467/) (2024)
- [Quickest Change Detection in Autoregressive Models](https://mlsanity.com/paper/2310.08789/) (2023)

## Built on by (most cited first, 4 of 4)

- [Score-Based Change-Point Detection and Region Localization for Spatio-Temporal Point Processes](https://mlsanity.com/paper/2602.04798/) (2026)
- [Two-Sample Testing via Path-based Inference](https://mlsanity.com/paper/2610.05684/) (2026)
- [Two-Sample Testing via Generative Processes](https://mlsanity.com/paper/2610.08277/) (2026)
- [Quickest Change Detection with Diffusion-Integrated Scores](https://mlsanity.com/paper/2610.12200/) (2026)

## Abstract (arXiv)

Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as powerful as their likelihood-based peers. Recent works consider generalizing the score-based Fisher divergence into a diffusion-divergence by transforming score functions via multiplication with a matrix-valued function or a weight matrix. In this paper, we extend the score-based hypothesis test and change-point detection stopping rule into their diffusion-based analogs. Additionally, we theoretically quantify the performance of these diffusion-based algorithms and study scenarios where optimal performance is achievable. We propose a method of numerically optimizing the weight matrix and present numerical simulations to illustrate the advantages of diffusion-based algorithms.