Fair Generation via Conditional-Independent Flow Matching

Yongsheng Chen, Tsai Hor Chan, Feng Wu, Yong Chen

Keywords: conditional independence;group fairness; conditional flow matching; conditional mutual information

TL;DR: We propose CI-CFM, a scalable, non-adversarial flow-matching method that enforces group fairness under conditional independence, provides auditable likelihoods, and achieves stronger fairness–accuracy trade-offs on synthetic and EHR benchmarks.

Abstract: We study conditional prediction under group fairness constraints requiring the model’s output $Y_{\mathrm{pred}}$ to be conditionally independent of sensitive attributes $Z$ given the true label $Y_{\mathrm{true}}$. Existing approaches—kernel penalties, adversarial debiasing, and mutual-information bounds—often scale poorly in high dimensions, are unstable to train, or lack auditable likelihoods. We propose **CI-CFM**, a conditional flow-matching generator coupled with density-based heads that score (i) the joint $p(Y_{\mathrm{pred}},Z,Y_{\mathrm{true}})$ and (ii) a factorized reference $q(Y_{\mathrm{pred}},Z',Y_{\mathrm{true}})$ together with their marginals $p(Z,Y_{\mathrm{true}})$ and $q(Z',Y_{\mathrm{true}})$. Our *divergence-difference* objective $\xi := D_{\mathrm{KL}}(p\|q)-D_{\mathrm{KL}}(p_{Z,Y_{\mathrm{true}}}\|q_{Z',Y_{\mathrm{true}}})$ equals the conditional mutual information $I(Y_{\mathrm{pred}};Z\mid Y_{\mathrm{true}})$ under mild assumptions, enabling single-stage, non-adversarial training with tractable likelihoods for auditing conditional independence and efficient single-/few-step sampling at inference. On synthetic data and EHR benchmarks (MIMIC-III/IV), CI-CFM improves accuracy while substantially reducing dependence on $Z$ given $Y_{\mathrm{true}}$; ablations confirm the effectiveness of the fairness weight schedule, variance-reduced estimator, and few-step ODE integration. Code is anonymously available at https://anonymous.4open.science/r/CICFM-0B67/.

Primary Area: generative models

Submission Number: 10222