noise schedule

The noise schedule is the recipe that decides how fast an image dissolves into static across the forward process — how much noise to add at each timestep. Think of it as the dial controlling the 'corruption speed.' Add noise too quickly and the early timesteps already destroy almost everything, leaving the network little useful signal to learn from; add it too slowly and you waste steps where the image is barely changed. A good schedule spreads the difficulty of denoising evenly across timesteps so the network spends its capacity where it matters.

Concretely the schedule is the sequence beta_1, ..., beta_T of per-step variances, or equivalently the cumulative quantities alpha_bar_t that determine the signal-to-noise ratio at each step. The original DDPM used a linear schedule, where beta grows linearly from a small value to a larger one. Nichol and Dhariwal later showed this destroys high-resolution information too abruptly near the end and proposed the cosine schedule, which keeps more signal in the middle timesteps and improves sample quality, especially at higher resolutions. The schedule is fixed before training and is shared by both the forward and reverse processes.

The schedule interacts with everything: it sets the signal-to-noise ratio that the network sees at each t, which influences whether epsilon-, x_0-, or v-prediction is best conditioned; it affects how many sampling steps you need; and at high resolution it must be shifted toward more noise (because nearby pixels are correlated, a fixed schedule effectively adds less destruction to a large image than a small one). Modern systems often re-derive or rescale the schedule for the resolution and latent space they operate in rather than blindly reusing DDPM's defaults.