Deep learning models for medical diagnosis frequently exhibit substantial performance disparities across sensitive subgroups (e.g., race, sex), even when average accuracy is high. While generative data augmentation offers a route to mitigate this, existing strategies are suboptimal; they typically address only one or two dependency channels between sensitive attributes and image features. We formalize the medical image formation process via a structural causal model, revealing that sensitive attributes actually influence image content through four distinct pathways-a structural complexity neglected by prior works. Based on this insight, we introduce CIPHER (Causal Intervention Pathways for Healthcare Equity and Robustness), a framework designed to systematically intervene on all four causal paths. To achieve this, CIPHER utilizes a diffusion backbone equipped with classifier-free guidance and null-text inversion. This technical design enables the faithful reconstruction of patient-specific anatomy while allowing for the precise, editable synthesis of counterfactuals required to break sensitive dependency chains. We tested CIPHER using chest X-ray and dermoscopy benchmarks across both standard and shifted data distributions. By employing a multi-pathway intervention strategy, our model reduced worst-group disparities by an average of 35.8% compared to disease-conditioned synthesis baselines, while also improving total diagnostic accuracy