Generative artificial intelligence (AI) systems are trained on large data corpora to generate new pieces of text, images, videos, and other media. There is growing concern that such systems may infringe on the copyright interests of training data contributors. To address the copyright challenges of generative AI, we propose a framework that compensates copyright owners proportionally to their contributions to the creation of AI-generated content. The metric for contributions is quantitatively determined by leveraging the probabilistic nature of modern generative AI models and using techniques from cooperative game theory in economics. This framework enables a platform where AI developers benefit from access to high-quality training data, thus improving model performance. Meanwhile, copyright owners receive fair compensation, driving the continued provision of relevant data for generative model training. Experiments demonstrate that our framework successfully identifies the most relevant data sources used in artwork generation, ensuring a fair and interpretable distribution of revenues among copyright owners.