This case illustrates what are probably features of prior Marchiafava Bignami syndrome. Subsequent history obtained from the patient, confirmed the presence of a period of severe binge drinking while depressed.

Prior to this, there was no history of alcohol abuse which would have made Marchiafava Bignami syndrome unlikely. Although predominantly white matter abnormalities, the appearances are not those of a leukodystrophy, CADASIL or MS/ADEM. HIV negative and non-immunosuppressed makes PML unlikely (and again I am not sure it involves the cc to this extent). That there was a vague history of hyponatremia does raise the possibility of extrapontine demyelination, however I am not aware of it involving the body of the corpus callosum (rather the splenium). 

Other possibilities include a leukoclastic vasculitis or encephalitis illness e.g. SLE, systemic sclerosis, etc.