Training advanced AI models requires large investments in computational resources, or compute. Yet, as hardware innovation reduces the price of compute and algorithmic advances make its use more efficient, the cost of training an AI model to a given performance falls over time - a concept we describe as increasing compute efficiency. We find that while an access effect increases the number of actors who can train models to a given performance over time, a performance effect simultaneously increases the performance available to each actor. This potentially enables large compute investors to pioneer new capabilities, maintaining a performance advantage even as capabilities diffuse. Since large compute investors tend to develop new capabilities first, it will be particularly important that they share information about their AI models, evaluate them for emerging risks, and, more generally, make responsible development and release decisions. Further, as compute efficiency increases, governments will need to prepare for a world where dangerous AI capabilities are widely available - for instance, by developing defenses against harmful AI models or by actively intervening in the diffusion of particularly dangerous capabilities.