  Protein structure prediction has reached revolutionary levels of accuracy on
single structures, yet distributional modeling paradigms are needed to capture
the conformational ensembles and flexibility that underlie biological function.
Towards this goal, we develop EigenFold, a diffusion generative modeling
framework for sampling a distribution of structures from a given protein
sequence. We define a diffusion process that models the structure as a system
of harmonic oscillators and which naturally induces a cascading-resolution
generative process along the eigenmodes of the system. On recent CAMEO targets,
EigenFold achieves a median TMScore of 0.84, while providing a more
comprehensive picture of model uncertainty via the ensemble of sampled
structures relative to existing methods. We then assess EigenFold's ability to
model and predict conformational heterogeneity for fold-switching proteins and
ligand-induced conformational change. Code is available at
https://github.com/bjing2016/EigenFold.
