Diffusion Models

Best for: Generative images/audio/video

How it works

Training corrupts data with a fixed forward Markov chain $q(x_t\mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t I\bigr)$ that gradually adds Gaussian noise until $x_T$ is pure noise. A network is then fit to reverse each step, $p_\theta(x_{t-1}\mid x_t)=\mathcal{N}(\mu_\theta(x_t,t),\sigma_t^2 I)$, which is equivalent to predicting the noise $\epsilon$ added at step $t$ via the simplified loss $\mathbb{E}_{x_0,\epsilon,t}\bigl\|\epsilon-\epsilon_\theta(x_t,t)\bigr\|^2$. Generation samples $x_T\sim\mathcal{N}(0,I)$ and applies the learned reverse transitions to denoise back to $x_0$.

Common fields

Image generation · design · media · simulation