Diffusion Family: A Unified View from Flow Models and SDEs
A Glimpse of Differential Equations Flow Models Example: Linear ODE If Adding Stochasticity to the Differential Equations A $dX_t$ Notation Constructing Training Targets for Flow & Diffusion Models from DE View Conditional and Marginal Distribution Path Conditional and Marginal Vector Field Side Note: Continuity Equation Extending to Stochastic Differential Equations Theorem: SDE Extension Trick Actually Optimizing for the Target Constructed Flow Matching! Example: Gaussian Path Score Matching! More on Score Matching: What to learn and what not to learn A Summary on Both Models from Differential Equations View References A Glimpse of Differential Equations We can view the target objects as vectors $z\in \mathbb{R}^d$, which is reasonable this notation is enought for many cases like images, videos or robots’ actions....