Linear Schedule

The linear schedule is the simplest and most straightforward noise schedule, introduced in the original DDPM paper. It adds noise at a constant rate throughout the diffusion process: $\beta_t$ grows uniformly from a small initial value to a final value. While easy to implement and reason about, it is quite inefficient for training, especially at higher resolutions. The issue is: the signal-to-noise ratio (SNR) plummets very quickly. By the time the forward process is only ~70% complete, the original image is practically indistinguishable from noise. This means the model wastes the last 30% of the process essentially adding noise to noise, which is an inefficient use of its training capacity. The cosine schedule was specifically designed to address this problem.