# Two-Sample Testing via Generative Processes

arXiv: https://arxiv.org/abs/2610.08277 · HTML: https://mlsanity.com/paper/2610.08277/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 57 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Builds on (most cited first, 14 of 14)

- [AutoGluon-Tabular: Robust and Accurate AutoML for Structured Data](https://mlsanity.com/paper/2003.06505/) (2020)
- [Your Diffusion Model is Secretly a Zero-Shot Classifier](https://mlsanity.com/paper/2303.16203/) (2023)
- [Text-to-Image Diffusion Models are Zero-Shot Classifiers](https://mlsanity.com/paper/2303.15233/) (2023)
- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Unsupervised Out-of-Distribution Detection with Diffusion Inpainting](https://mlsanity.com/paper/2302.10326/) (2023)
- [On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity](https://mlsanity.com/paper/2506.03719/) (2025)
- [Information-Theoretic Diffusion](https://mlsanity.com/paper/2302.03792/) (2023)
- [Classification accuracy as a proxy for two sample testing](https://mlsanity.com/paper/1602.02210/) (2016)
- [A Witness Two-Sample Test](https://mlsanity.com/paper/2102.05573/) (2021)
- [Diffusion-Based Hypothesis Testing and Change-Point Detection](https://mlsanity.com/paper/2506.16089/) (2025)
- [Midpoint Generative Models](https://mlsanity.com/paper/2605.29920/) (2026)
- [Zero-Flow Two-Sample Tests](https://mlsanity.com/paper/2607.21542/) (2026)
- [Two-Sample Testing via Path-based Inference](https://mlsanity.com/paper/2610.05684/) (2026)

## Abstract (arXiv)

Deciding whether two samples come from the same distribution is a classical problem in statistics, and generative transport offers a new way to approach it. We build a stochastic interpolant directly between the two samples and observe that, for a symmetric schedule, its law is invariant under the time reflection t mapsto 1-t whenever the two distributions coincide. We therefore test whether the marginals at times t and 1-t agree by computing their Jensen--Shannon divergence. Both marginals are explicit mixtures over all cross-pairs of observations, so nothing is learned, and permutation calibration gives an exact finite-sample level. For Gaussian noise, this divergence equals a time integral that pairs the reflection defects of the velocity field and of the score, so the test compares transport dynamics rather than endpoints alone. With a narrow-plus-broad noise design, the test attains the minimax separation rate n-2s/(4s+d) over bounded, compactly supported densities whose difference has Sobolev smoothness s > 3d/4, with no lower bound on the densities. Fusing a dyadic grid of noise scales through their permutation ranks, without sample splitting, preserves exact level and adapts to unknown s at an iterated-logarithmic cost. Empirically, the test matches or outperforms state-of-the-art kernel two-sample tests.