Counterfactual Generation via Flow Matching: Coupling-Sensitive End-to-End Rates

2026-10-01

AI Summary

This study addresses the problem of generating counterfactual outcomes under hypothetical interventions from observational data. To this end, it proposes a flow matching framework that integrates doubly robust training with coupling learning to enable end-to-end counterfactual generation, while introducing Gaussian smoothed interpolation and stochastic samplers to enhance inference efficiency. Theoretically, the work establishes a coupling-sensitive KL error bound, demonstrating its dependence on displacement moments rather than global regularity, and provides finite-step convergence guarantees. Empirically, experiments on synthetic and image benchmarks validate these theoretical findings, revealing that stochastic samplers significantly outperform deterministic ODE samplers under limited computational budgets.

Abstract

Counterfactual generation seeks to sample outcomes under a hypothetical intervention or decision using observational data collected under the factual assignment mechanism. We develop a flow-matching approach that combines a sample-split, doubly robust training objective with a learned coupling between observed source outcomes and target outcomes drawn from a fitted conditional outcome model. To enable finite-step generation, we leverage a score-corrected stochastic sampler based on a Gaussian-smoothed interpolation. Our main theoretical contribution is a coupling-sensitive KL bound for constant-step Euler discretization: the error is controlled by moments of the source--target displacement under the chosen coupling, rather than by global uniform regularity of the velocity field, and has near-linear dependence on the ambient dimension. We also establish finite-sample non-parametric guarantees for the learned velocity and score fields when both the conditional outcome model and the source-target coupling are estimated from data. These bounds separate approximation, coupling-replacement, nuisance-estimation, generalization, and Monte Carlo errors and, combined with the sampler analysis, yield an end-to-end guarantee for counterfactual generation. Experiments on synthetic and semi-synthetic image benchmarks support the coupling-dependent theory and show that, at finite discretization budgets, the stochastic sampler can outperform the corresponding deterministic ODE sampler.

Problem

• Counterfactual Generation
• Flow Matching
• Causal Inference
• Coupling-Sensitive Error Bound

Innovation

• Counterfactual Generation
• Flow Matching
• Coupling-Sensitive KL Bound
• Score-Corrected Stochastic Sampler
• Doubly Robust Training