Foundation models (e.g., GPT-4 and Llama 3.1) are at the epicenter of artificial intelligence (AI), driving technological innovation and billions of dollars in investment. This has sparked widespread demands for regulation. Central to the debate about how to regulate foundation models is the process by which foundation models are released (1)—whether they are made available only to the model developers, fully open to the public, or somewhere in between. Open foundation models can benefit society by promoting competition, accelerating innovation, and distributing power. However, an emerging concern is whether open foundation models pose distinct risks to society (2). In general, although most policy proposals and regulations do not mention open foundation models by name, they may have an uneven impact on open and closed foundation models. We illustrate tensions that surface—and that policy-makers should consider—regarding different policy proposals that may disproportionately damage the innovation ecosystem around open foundation models.