Statistical Inference via Generative Models: Flow Matching and Causal Inference

TL;DR

This paper reinterprets generative AI as a statistical tool for nonparametric high-dimensional distribution learning, emphasizing interpretability, principled sampling, and causal inference, with applications to complex structured data.

Contribution

It introduces a statistical framework for generative models using flow matching, connecting distributional deformation with causal inference and structured data analysis.

Findings

Flow matching extends score matching to transport paths.

Generative models enable principled missing-data imputation.

Applications demonstrate integration into survival analysis and causal inference.

Abstract

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book reinterprets generative AI in the language of statistics, using flow matching as a central example. The key idea is that generative models should be understood not merely as devices for producing plausible data, but as methods for the nonparametric learning of high-dimensional probability distributions. From this viewpoint, missing-data imputation becomes principled sampling from learned conditional distributions, counterfactual analysis becomes the estimation of intervention distributions, and distributional dynamics become statistically analyzable objects. Mathematically, flow matching represents distributional deformation through the continuity equation and a time-dependent velocity field, thereby extending score matching from the learning of static score fields to the learning of transport paths themselves. Building on this foundation, the book develops a statistical framework in which generative models are used to estimate nuisance components while inferential validity is maintained through orthogonalization and cross-fitting in the spirit of double/debiased machine learning. Applications to survival analysis, censoring, missingness, and causal inference show how generative models can be integrated into statistical inference for structured high-dimensional problems.