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Diffusion models generate data by sampling latent noisy states: forward diffusion creates xt from x0, and reverse diffusion reconstructs x0 from xT.
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).
Diffusion models generate data by sampling latent noisy states: forward diffusion creates xt from x0, and reverse diffusion reconstructs x0 from xT.
In DDPM, a neural network parameterizes the reverse transition distribution pθ(xt−1|xt) and is trained via variational inference to make the generated distribution pθ(x0) match q(x0).
Score-based and DDPM formalisms are equivalent: the network learns an approximation to the score ∇x ln ρt (or equivalently predicts noise), enabling reverse sampling via (S)DE-based denoising.
Because the reverse process can be run with different sampling strategies (e.g., DDIM), diffusion models can trade off sampling speed versus quality while still using the same latent-variable denoising mechanism.
A generative model that introduces hidden variables and samples them to produce observable data.
A Markov process that starts from x0 and repeatedly adds Gaussian noise to produce xt, eventually approaching N(0, I).
A learned process that starts from xT ~ N(0, I) and iteratively denoises to obtain x0 distributed like the training data.
A diffusion framework that learns the reverse transitions pθ(xt−1|xt) using a neural network and trains it with variational inference.
The neural network (often a U-Net or transformer) that predicts noise or denoising parameters from xt and the timestep t.
The gradient of the log-density, ∇x ln ρt, indicating how to move in data space to increase likelihood under the noisy distribution ρt.
A score-based model that learns the score ∇x ln ρt for noise levels that depend on time (or noise scale).
A training approach that optimizes a lower bound on likelihood, commonly used to fit diffusion models such as DDPM.
A variant that enables fewer reverse steps by using a deterministic or partially deterministic reverse process, trading quality for speed.
“Can you explain what "Diffusion models generate data by sampling latent noisy states: forward diffusion creates xt from x0, and reverse diffusion reconstructs x0 from xT." means in simple terms?”