Peer-to-peer (P2P) networks are fast emerging as a viable and cost effective alternative for content delivery on the Internet. By offering rebates to users who share content with others, incentives can be provided to address the well-documented problem of free riding. A primary value proposition of P2P networks is their ability to scale well and facilitate fast distribution of digital products. While the fast diffusion of products in P2P networks has generated substantial interest in P2P, rigorous theoretical studies of the diffusion process have been in absence. Our paper provides one of the first analytical studies of the diffusion process in P2P networks. Starting with an analogy between P2P diffusion and epidemic diffusion, we develop a stochastic diffusion model for flat P2P networks. We find that product diffusion, in P2P networks is likely to follow classic S-shaped processes. Next, we develop a deterministic approximation that is computationally efficient. The model allows a content publisher to analyze the diffusion process, evaluate the impact of offering rebates on product diffusion and also determine the optimal rebate to offer by trading off the reduced margins with the faster diffusion of the product. Finally, we expand our study to account for generation of multiple requests and forwarding of requests in P2P networks. The analytical models presented in this paper serve as a starting point for rigorous modeling and study of content diffusion in P2P networks.