generate new ones unseen during training. Older models, like generative adversarial networks or GANs, attempted to learn P data directly, but their output quality suffered. The issue is, this density is extremely complex to learn in one go. It literally makes a judgment about every possible combination of pixels. So, to make this problem more tractable, modern methods, like flow matching and diffusion, discover P data progressively. They start with a much simpler density P0, chosen programmatically, and gradually evolve it over time. Generative modeling happens in a fictitious time interval from T equals 0 to T equals 1. It's like a progress bar that moves a density PT between the source P0 and the destination P data. In reality, since we don't know the real P data, we'll guide the model towards an approximation of it that concentrates probability mass around the training points. This is the target density P1.