When approaching the methods used in de-novo protein design, one is quickly confronted with a plethora of overlapping formulations of what looks superficially like “the same thing”. One paper trains an $\boldsymbol{\epsilon}$-prediction network with a simple MSE loss; another trains a score network with a stochastic-differential-equation justification; a third trains a clean-data predictor under yet another schedule. Each formulation carries its own notation, its own variance schedule, and its own sampler. Qualitatively, this zoo of formulations is doing the same thing: it starts from some unstructured noise and iteratively refines it to eventually produce a protein structure similar (but different!) to other proteins we have experimentally determined in the past. What is not immediately obvious to a newcomer is that all of these formulations are historical descendants of a small number of foundational ideas, and that essentially every architectural and algorithmic decision in a modern protein-design diffusion model has a specific paper of origin and a specific motivation for being there.

This post is my attempt to put these formulations onto a single timeline. I trace the trajectory of the field through four foundational works: DDPM (Ho et al., 2020), DDIM (Song et al., 2021a), the score-based SDE unification (Song et al., 2021b), and EDM (Karras et al., 2022), explaining at each step what specific problem with the previous formulation the next paper was attacking and how the new formulation generalises or simplifies the old one. The goal is coherent motivation rather than exhaustive coverage; the reader interested in implementation details is referred to the original papers and the references at the end.