Fig. 2: FoldingDiff generates realistic distributions of bond and dihedral angles.

a FoldingDiff iteratively denoises the underlying angles from an unfolded structure (left) towards angles corresponding to a final folded structure (right). Shifts in angle distributions, e.g., of an example dihedral \(\left(\psi \right)\), accordingly occur over this generative process. b Distributions of individual angles for backbones sampled from FoldingDiff (Sampled, orange), compared to that of natural backbones (Test, blue). Sampling was repeated 10 times for each backbone length \(l\in [{{{{\mathrm{50,128}}}}})\) yielding a total of 780 generated backbones. c Co-occurrence of \(\phi\) and \(\psi\) dihedral angles, visualized as Ramachandran plots, over natural proteins (left) and generations sampled from FoldingDiff (right). Arrows indicate \(\left(\phi,\psi \right)\) value sets corresponding to three major secondary structure elements: right-handed \(\alpha\) helices (\(\alpha\) helix, RH), left-handed \(\alpha\) helices (\(\alpha\) helix, LH), and \(\beta\) sheets (\(\beta\) sheet). Faint vertical/horizontal lines are artifacts of replacing and imputing null values.