Diffusion and Score-Based Generative Models

Diffusion models as latent variable generators

Diffusion models can be viewed as latent variable generators: they introduce a sequence of hidden variables (noisy versions of the data) and learn a probabilistic process that maps between the data distribution and a simple prior. The forward diffusion process gradually corrupts a sample x0 by adding Gaussian noise over T steps, producing xt that eventually approaches a standard Gaussian N(0, I). The reverse (generative) process then uses a learned denoising model to iteratively remove noise, starting from a latent variable xT sampled from N(0, I), until it reconstructs a sample from the target data distribution q(x0).

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Forward diffusion process adding noise

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