DDPM trains a network to predict the added noise epsilon rather than the clean sample or the reverse mean

The optimal reverse-process mean can be expressed in terms of either x_0 (predict the clean image) or the noise epsilon_t (predict what was added). Ho et al. (2020) reparameterize so the network epsilon_theta(x_t,t) predicts the Gaussian noise that was added to x_0 to produce x_t — x_t is available as input at training time. The predicted mean is then computed as (1/sqrt(alpha_t))*(x_t - (1-alpha_t)/sqrt(1-alpha_bar_t)*epsilon_theta). This shifts the learning problem from predicting a potentially complex signal to predicting simple isotropic Gaussian noise, which is easier to optimise. At inference, each denoising step subtracts the predicted noise contribution.

Examples

In practice: given a noisy training image x_t, the U-Net predicts the noise map epsilon that was added, not the clean image. The loss is MSE between predicted and actual noise.

Assessment

In DDPM, what does the network learn to predict: x_0, or epsilon_t? Explain why this choice is made and how the predicted quantity is used to compute the reverse-step mean.