Diffusion Models Learning Path

Diffusion models as latent variable generative models

Diffusion models (also called diffusion-based or score-based generative models) are latent variable generative models that learn to generate data by simulating a gradual corruption process and then reversing it. They consist of a forward diffusion process that repeatedly adds Gaussian noise to data until it becomes (approximately) standard Gaussian, and a reverse sampling process that uses a learned neural network (“backbone”) to denoise step-by-step and recover samples from the original data distribution. In the DDPM formulation, the forward process is a Markov chain with a fixed noise schedule, while the reverse process is parameterized by a neural network that predicts the mean (and often variance) of the denoising distribution at each time step. Training is typically done via variational inference, which can be expressed as learning to predict noise (or equivalently the score/gradient of the log-density). In the score-based view, the network is trained to approximate the score function ∇x log ρt of the noisy data distribution at noise level t, enabling generation by integrating a reverse-time stochastic differential equation (SDE) or its discrete-time counterpart. A key result is the equivalence between DDPMs and score-based generative models: with appropriate parameterizations and in the continuous limit, the denoising network’s predicted noise corresponds to the score function, so both formalisms describe the same underlying generative mechanism. This equivalence also explains why diffusion models can be implemented with different but related architectures and sampling strategies (e.g., faster samplers like DDIM), while still relying on the same learned denoising/score estimation principle.

0/2 modes complete

Forward diffusion process and noise addition

0/2 modes complete