AI RESEARCH
A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
arXiv CS.CL
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ArXi:2605.22586v1 Announce Type: cross This tutorial develops diffusion models from the viewpoint of differential equations. We begin with the conditional Gaussian forward process and show that this path admits both an ordinary differential equation (ODE) representation and a stochastic differential equation (SDE) representation. Averaging the conditional process over the data distribution then yields marginalized forward ODE and SDE formulations that transport the data distribution $p_0=p_{\mathrm{data}}$ to a Gaussian prior $p_1=\mathcal{N}(0,I.