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Recent advancements in generative AI, particularly diffusion models, have proven valuable for text-to-image synthesis. In health care, these models offer immense potential in generating synthetic datasets and aiding medical training. Despite these strong performances, it remains uncertain whether the image generation quality is consistent across different demographic subgroups. To address this, we conduct a comprehensive analysis of fairness in medical text-to-image diffusion models. Evaluations of the Stable Diffusion model reveal substantial disparities across gender, race, and ethnicity. To reduce these biases, we propose FairDiffusion, an equity-aware latent diffusion model that improves both image quality and the semantic alignment of clinical features. In addition, we design and curate FairGenMed, a dataset tailored for fairness studies in medical generative models. FairDiffusion is further assessed on HAM10000 (dermatoscopic images) and CheXpert (chest x-rays), demonstrating its effectiveness in diverse medical imaging modalities. Together, FairDiffusion and FairGenMed advance research in fair generative learning, promoting equitable benefits of generative AI in health care.