Diffusion Models: How Do You Learn to Run the Noising Process Backward? | Stanford CS229 Lecture 11
Each forward step multiplies the data by √(1−β_t) and adds Gaussian noise with variance β_t. Unrolled, x_t = √ᾱ_t·x_0 + √(1−ᾱ_t)·ε̂_t, and nothing here is learned. The reverse direction is learned with a Gaussian p_θ(x_{t−1}|x_t): apply last lecture's ELBO to the whole trajectory, split it with the KL chain rule, and the loss at each step is ‖μ̃_t(x_t,x_0) − μ_θ(x_t,t)‖²/(2β̃_t). The lecture stops at this expression; simplifying it into noise prediction is left for Lecture 12.