Diffusion models are becoming increasingly popular in synthetic data generation and image editing applications. However, these models can amplify existing biases and propagate them to downstream applications. Therefore, it is crucial to understand the sources of bias in their outputs. In this paper, we investigate the presence of bias in diffusion-based face generation models with respect to attributes such as gender, race, and age. Moreover, we examine how dataset size affects the attribute composition and perceptual quality of both diffusion and Generative Adversarial Network (GAN) based face generation models across various attribute classes. Our findings suggest that diffusion models tend to worsen distribution bias in the training data for various attributes, which is heavily influenced by the size of the dataset. Conversely, GAN models trained on balanced datasets with a larger number of samples show less bias across different attributes.