Chest X-rays (CXR) are essential for diagnosing a variety of conditions, but when used on new populations, model generalizability issues limit their efficacy. Generative AI, particularly denoising diffusion probabilistic models (DDPMs), offers a promising approach to generating synthetic images, enhancing dataset diversity. This study investigates the impact of synthetic data supplementation on the performance and generalizability of medical imaging research. The study employed DDPMs to create synthetic CXRs conditioned on demographic and pathological characteristics from the CheXpert dataset. These synthetic images were used to supplement training datasets for pathology classifiers, with the aim of improving their performance. The evaluation involved three datasets (CheXpert, MIMIC-CXR, and Emory Chest X-ray) and various experiments, including supplementing real data with synthetic data, training with purely synthetic data, and mixing synthetic data with external datasets. Performance was assessed using the area under the receiver operating curve (AUROC). Adding synthetic data to real datasets resulted in a notable increase in AUROC values (up to 0.02 in internal and external test sets with 1000% supplementation, p-value less than 0.01 in all instances). When classifiers were trained exclusively on synthetic data, they achieved performance levels comparable to those trained on real data with 200%-300% data supplementation. The combination of real and synthetic data from different sources demonstrated enhanced model generalizability, increasing model AUROC from 0.76 to 0.80 on the internal test set (p-value less than 0.01). In conclusion, synthetic data supplementation significantly improves the performance and generalizability of pathology classifiers in medical imaging.