Two-Sample Testing via Path-based Inference

2026-10-05

AI Summary

This study addresses the challenge of efficiently determining whether two datasets originate from the same distribution via two-sample testing. It proposes leveraging generative model dynamics for statistical inference by connecting data distributions to a Gaussian bottleneck through stochastic interpolation. The authors demonstrate that the null hypothesis is equivalent to reflection symmetry along the generative path, and construct a test statistic based on discrepancies in denoising velocity fields. Robustness is achieved through permutation calibration and Jeffreys divergence-weighted aggregation. This work establishes a theoretical connection between generative path symmetry and two-sample testing, extending generative models into the domain of statistical inference. Empirical evaluations on synthetic and image benchmarks show that, under identical sample budgets, the proposed method improves test power by up to 33 percentage points over state-of-the-art baselines.

Abstract

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 networks and consistent when the fields are learned accurately. On a synthetic benchmark and three image benchmarks, the proposed tests improve power over the strongest baseline by up to 33 percentage points at an equal total sample budget, with the best choice of regression representation and path weighting depending on the data modality. These results show that generative paths provide a principled representation for statistical testing, extending stochastic-interpolant models beyond generation.

Problem

• Two-sample testing
• Deep generative models
• Stochastic interpolants
• Statistical inference

Innovation

• Two-Sample Testing
• Stochastic Interpolants
• Generative Paths
• Jeffreys Divergence
• Denoiser Velocity Fields