We present novel approaches involving generative adversarial networks and diffusion models in order to synthesize high quality, live and spoof fingerprint images while preserving features such as uniqueness and diversity. We generate live fingerprints from noise with a variety of methods, and we use image translation techniques to translate live fingerprint images to spoof. To generate different types of spoof images based on limited training data we incorporate style transfer techniques through a cycle autoencoder equipped with a Wasserstein metric along with Gradient Penalty (CycleWGAN-GP) in order to avoid mode collapse and instability. We find that when the spoof training data includes distinct spoof characteristics, it leads to improved live-to-spoof translation. We assess the diversity and realism of the generated live fingerprint images mainly through the Fr\'echet Inception Distance (FID) and the False Acceptance Rate (FAR). Our best diffusion model achieved a FID of 15.78. The comparable WGAN-GP model achieved slightly higher FID while performing better in the uniqueness assessment due to a slightly lower FAR when matched against the training data, indicating better creativity. Moreover, we give example images showing that a DDPM model clearly can generate realistic fingerprint images.