Square Root Schedule

The square-root schedule front-loads noise more aggressively than the linear schedule but less than exponential approaches. The $\bar\alpha_t$ curve drops steeply at the beginning—the model is quickly pushed into challenging denoising territory—then gradually levels off as $t$ approaches $T$. This shape prioritizes learning coarse, global structure early while spending more time on the nuanced late-stage transitions. It can be seen as a compromise between the uniform pacing of linear and the delayed-difficulty approach of cosine.