  The interaction of a protein with its environment can be understood and
controlled via its 3D structure. Experimental methods for protein structure
determination, such as X-ray crystallography or cryogenic electron microscopy,
shed light on biological processes but introduce challenging inverse problems.
Learning-based approaches have emerged as accurate and efficient methods to
solve these inverse problems for 3D structure determination, but are
specialized for a predefined type of measurement. Here, we introduce a
versatile framework to turn raw biophysical measurements of varying types into
3D atomic models. Our method combines a physics-based forward model of the
measurement process with a pretrained generative model providing a
task-agnostic, data-driven prior. Our method outperforms posterior sampling
baselines on both linear and non-linear inverse problems. In particular, it is
the first diffusion-based method for refining atomic models from cryo-EM
density maps.
