What is the effect of linear versus cosine beta schedules?

The choice between linear and cosine beta schedules in diffusion models affects how noise is added during training and sampling, which impacts model performance and output quality. A beta schedule determines the rate at which noise is introduced across the diffusion process’s timesteps. A linear schedule increases noise uniformly, while a cosine schedule adjusts the noise increment based on a cosine function, leading to slower changes at the start and end of the process.

A linear beta schedule applies noise at a constant rate across all timesteps. For example, if the beta values range from 0.0001 to 0.02 over 1,000 steps, each step adds a fixed amount of noise. This simplicity makes it easy to implement and interpret. However, this uniform approach can lead to abrupt changes in later stages of diffusion, where high noise levels might overwhelm subtle details in the data. In image generation, this might result in blurry outputs or artifacts, as the model struggles to refine fine-grained features when noise increases too rapidly. The linear schedule is often used in baseline implementations of diffusion models (e.g., DDPM) due to its straightforward design, but it may require more timesteps to achieve high-quality results.

In contrast, a cosine beta schedule slows the rate of noise increase at the beginning and end of the process while accelerating it in the middle. For instance, the schedule might use a cosine function to map timesteps to beta values, ensuring smaller changes early (preserving initial structure) and later (allowing finer adjustments during denoising). This approach aligns better with human perception, as it prioritizes gradual refinement in the final steps. For example, in the Improved DDPM paper, researchers found that cosine schedules produce sharper images with fewer artifacts compared to linear schedules. The slower start gives the model time to learn coarse features, while the slower end helps retain details during sampling. However, cosine schedules may require careful tuning of hyperparameters (e.g., offset parameters) to avoid oversmoothing or instability in certain datasets.

From a practical standpoint, developers should consider the trade-offs between simplicity and performance. Linear schedules are easier to debug and faster to train but may underperform on complex tasks. Cosine schedules often yield better results but require more computational resources and parameter tuning. For example, in text-to-image models, cosine schedules are preferred for high-resolution outputs, while linear might suffice for low-res prototyping. The choice ultimately depends on the use case: if quality is critical, cosine is worth the effort; if speed or simplicity matters more, linear is a viable starting point.