Asked about The maths of denoising diffusion, just enough
Write down the diffusion training objective and explain it.
An answer that works
Sample a clean example, a random step t and Gaussian noise, form x_t as sqrt(alphabar_t) times the clean example plus sqrt(1 minus alphabar_t) times the noise, and train the model to predict that noise with a squared error loss.
Then they push further
Why can training jump straight to any step?
The sum of Gaussian noise steps is itself Gaussian with a known variance, so x_t has a closed form given x_0. There is no need to simulate the chain during training.
How does classifier-free guidance work?
The model is trained with and without the condition. At sampling, the unconditional prediction is pushed further in the direction of the conditional one by a guidance weight, strengthening adherence to the prompt at the cost of diversity.
What gets marked up
Marked up for the closed-form forward process, the noise-prediction objective and the guidance formula.
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