Significance Advanced, non-Gaussian diffusion-weighted imaging (DWI) measurements that probe white matter microstructure across a range of diffusion contrasts were sensitive to diagnosis-specific abnormalities in schizophrenia and independently predicted patient–control differences in processing speed. Two orthogonal statistical factors extracted from DWI measurements explain most of diagnosis-related differences in processing speed. Moreover, DWI measurements explained a similar degree of variance in processing speed in patients and controls separately and in siblings of patients. This link remains contiguous across the diagnostic boundary and was not driven by subject selection or antipsychotic medication. The non-Gaussian diffusion white matter metrics are promising surrogate imaging markers for modeling cognitive deficits and perhaps, guiding treatment development.