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Describe the forward and reverse processes in diffusion models.

hard

Answer

  • Forward (q): gradually add Gaussian noise to the data over T steps until it becomes ~ N(0, I).
  • Fixed, no learning.
  • Closed-form: xt  =  sqrt(αbart)x0  +  sqrt(1    αbart)ϵx_{t}\; = \;\mathrm{sqrt}(\alpha_{\mathrm{bar}}t) \cdot x_{0}\; + \;\mathrm{sqrt}(1\; - \;\alpha_{\mathrm{bar}}t) \cdot \epsilon.
  • Reverse (pθ)(p{\theta}): learn to denoise step-by-step, reversing q.
  • Train by minimizing EtE_{t},x0x_{0},eps [eps    epsθ(xt,  t)2][ \mid \mid \mathrm{eps}\; - \;\mathrm{eps}{\theta}(x_{t}, \;t) \mid \mid ^{2}] — the network predicts the noise added at each step.
  • At sampling, start from Gaussian noise and denoise for T (or fewer, with DDIM) steps.
Check yourself — multiple choice
  • Diffusion doesn't use noise
  • Forward: add noise until Gaussian; reverse: learn to denoise step-by-step; train ε_θ to predict added noise
  • Diffusion trains an encoder-decoder
  • Same as GAN

Diffusion: add noise → train to reverse via noise prediction (DDPM).

#diffusion#generative

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