Zero-Flow Two-Sample Tests
Abstract
Motivated by the success of modern flow-based generative models in modeling complex data, we study two-sample testing through the lens of flow-based methods. We propose the Zero-Flow Two-Sample Test (ZF2ST), built on the zero-flow criterion, which characterizes distributional equality through a time-reversal antisymmetry of a learnable velocity field. We extend this criterion and further develop the Zero-Flow Discrepancy, an identifying discrepancy that controls the Wasserstein distance, and derive a variational representation in terms of a witness function. This representation naturally leads to a witness-based test whose power is governed by the signal-to-noise ratio (SNR), allowing direct power maximization for witness learning. ZF2ST learns the witness on one data split and performs testing on held-out samples, thereby maintaining Type-I error control and admitting a simple asymptotic null distribution. Experimentally, ZF2ST performs competitively across various synthetic and real-world benchmarks, while showing particularly strong performance in distinguishing image distributions from different sources.
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BibTeX
@misc{wang2026zeroflow,
title = {{Zero-Flow Two-Sample Tests}},
author = {Yakun Wang and Leyang Wang and Song Liu and Taiji Suzuki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.21542},
eprint = {2607.21542},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.21542},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Zero-Flow Two-Sample Tests
AU - Yakun Wang
AU - Leyang Wang
AU - Song Liu
AU - Taiji Suzuki
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2607.21542
UR - https://arxiv.org/abs/2607.21542
AB - Motivated by the success of modern flow-based generative models in modeling complex data, we study two-sample testing through the lens of flow-based methods. We propose the Zero-Flow Two-Sample Test (ZF2ST), built on the zero-flow criterion, which characterizes distributional equality through a time-reversal antisymmetry of a learnable velocity field. We extend this criterion and further develop the Zero-Flow Discrepancy, an identifying discrepancy that controls the Wasserstein distance, and derive a variational representation in terms of a witness function. This representation naturally leads to a witness-based test whose power is governed by the signal-to-noise ratio (SNR), allowing direct power maximization for witness learning. ZF2ST learns the witness on one data split and performs testing on held-out samples, thereby maintaining Type-I error control and admitting a simple asymptotic null distribution. Experimentally, ZF2ST performs competitively across various synthetic and real-world benchmarks, while showing particularly strong performance in distinguishing image distributions from different sources.
ER -