Wolfram syndrome (WFS or WFS1, OMIM 222300) is typically caused by two mutations and inherited in an autosomal recessive manner. Cases of typical WFS have been reported where only one mutation was detected (Hansen L, 2005 - PMID: 16151413). WFS1-related disorders also include WFS-like disorder and WFS1-related low-frequency sensory hearing loss (LFSNHL, also known as DFNA6 or DFNA14 or DFNA38, OMIM 600965), both of which are inherited in an autosomal dominant manner. WFS mutations are in general inactivating ‘loss-of-function’ mutations as nonsense or frame shift mutations, whereas mutations found in combination with autosomal dominant LFSNHL are small noninactivating ‘gain-of-function’ (Hansen L et al 2005, PMID: 16151413).
Indeed, Cryns K (2002, PMID: 12955714) found out that among the WFS1 mutations reported in LFSNHI, none is expected to lead to premature protein truncation, and the majority cluster in the C-terminal protein domain. In contrast, he found out that 64% of the Wolfram syndrome mutations are inactivating and thus concluded that only non-inactivating mutations in WFS1 are responsible for non-syndromic low-frequency hearing impairment. One additional interesting publication on this is always from Cryns K (2003, PMID: 12073007). 
Fundoscopy showing pale disc
It would be important to highlight that Wolfram syndrome 2 (WFS2, OMIM 604928), which is caused by mutation in the CISD2 gene, is a differnt form of the syndrome. This was descriebd by El-Shanti et al. (2000, PMID: 10739754) in patients with features in addition to those previously described in Wolfram syndrome, without diabetes insipidus and with profound upper gastrointestinal ulceration and bleeding in several cases.
For references: see text.
