Two-Sample Testing via Path-based Inference

Eshant English, Wei-Cheng Lai, Yanfeng Yang, Kenji Fukumizu, Taiji Suzuki +1

Modern deep generative models are primarily studied for their ability to generate realistic samples, yet the generative dynamics they learn can also serve as objects of statistical inference. We develop this idea for two-sample testing, the problem of deciding whether the same distribution generated two finite datasets. Using stochastic interpolants, we connect both distributions to a shared Gaussian bottleneck, so that each half of the resulting path is a Gaussian channel acting on a single population. We prove that the null hypothesis holds if and only if the population denoiser, or equivalently, the velocity fields of the two halves, coincide at any single noise level, which amounts to a reflection symmetry of the path about the bottleneck. Deviations from this symmetry yield a continuum of two-sample witnesses, which we estimate via held-out regression risks on learned denoisers and velocities and aggregate along the path; under an information-theoretic weighting, the aggregated discrepancy equals the Jeffreys divergence between the noise-smoothed distributions. Calibrating the resulting statistics by permutation yields tests that are valid in finite samples for any trained…