Diffusion forward and reverse processes

WHAT THIS TESTS: Whether you can separate the fixed corruption process from the learned generative process and state the concrete training objective.

A GOOD ANSWER COVERS: The forward process is a fixed schedule that gradually adds small amounts of Gaussian noise to a real image over many timesteps. It has no learnable parameters; the noise variances follow a predefined schedule. After enough steps the image is statistically indistinguishable from pure Gaussian noise. The reverse process is the generative direction: starting from random noise, the model takes many small denoising steps to walk back toward a clean sample. This reverse direction is what the neural network learns. In the standard formulation the network receives a noisy image and its timestep and is trained to predict the noise that was added, using a simple mean-squared error between predicted and actual noise. Predicting the noise is equivalent to estimating the score, the gradient of the log density, which tells the sampler which direction reduces noise.

COMMON WRONG ANSWERS: Saying the forward process is learned; claiming the model predicts the final clean image directly in one step rather than the per-step noise; conflating diffusion with GANs and introducing a discriminator; forgetting that the timestep is an input so a single network handles all noise levels.

LIKELY FOLLOW-UPS: Why train on a randomly sampled timestep each iteration? Why is predicting noise preferred over predicting the clean image? How does the reparameterization let you jump to any noisy timestep in one step? What is the link to score-based models?

ONE CONCRETE EXAMPLE: Take a photo, pick timestep 400 of 1000, add the corresponding amount of Gaussian noise in closed form, and feed the noisy image plus the number 400 to the network. It outputs an estimate of the exact noise tensor that was added; the loss is the squared error to the true noise. At generation time you start from pure noise and repeatedly subtract the predicted noise, gradually revealing a coherent image.