Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for performing protein structure prediction. In one aspect, a method comprises, at each of one or more iterations: determining an alternative predicted structure of a given protein defined by alternative values of structure parameters; processing, using a geometry neural network, a network input comprising: (i) a representation of a sequence of amino acid residues in the given protein, and (ii) the alternative values of the structure parameters, to generate an output characterizing an alternative geometry score that is an estimate of a similarity measure between the alternative predicted structure and the actual structure of the given protein.