Diffusion models from scratch, from a new theoretical perspective \[\newcommand{\Kset}{\mathcal{K}} \newcommand{\distK}{ {\rm dist}_{\Kset} } \newcommand{\projK}{ {\rm proj}_{\Kset} } \newcommand{\eps}{\epsilon} \newcommand{\Loss}{\mathcal{L}} \newcommand{\norm}[1]{\left\lVert #1 \right\lVert} \newcommand{\R}{\mathbb{R}} \DeclareMathOperator{\softmin}{softmin} \DeclareMathOperator{\distop}{dist}\] Diffusion models have recently produced impressive results in generative modeling, in particular sa...