Neighborhood-Guided Flow Matching for Potential Outcome Distributions

Recent work in causal inference has increasingly focused on modeling conditional distributions of potential outcomes, which capture outcome variability beyond conditional means. Balanced representation learning aims to mitigate selection bias in observational data, but representation alignment alone does not ensure that fine outcome variations are preserved. To address this challenge, we propose a unified framework that couples representation balancing with neighborhood-guided flow matching. Our method encourages alignment between treatment groups in latent space and uses observed outcomes from covariate neighbors in the target treatment arm as flow-matching endpoints, while conditioning the velocity field on the individual's learned representation and the target treatment. By weighting neighborhood supervision according to local treatment support, the model borrows outcome information where suitable neighboring observations are available. Under standard identification and smoothness assumptions, we show that neighborhood supervision targets a local mixture of conditional potential outcome distributions and bound its deviation from the true distribution. Experiments demonstrate the effectiveness of our method in conditional distribution recovery on synthetic data and treatment-effect estimation on standard causal benchmarks.