BACKGROUND: Processing of degraded speech is a promising model for understanding communication under challenging listening conditions, core auditory deficits and residual capacity for perceptual learning and cerebral plasticity in major dementias. METHODS: We compared the processing of sine-wave-degraded speech in 26 patients with primary progressive aphasia (non-fluent, semantic, and logopenic variants), 10 patients with typical Alzheimer's disease and 17 healthy control subjects. Participants were required to identify sine-wave words that were more predictable (three-digit numbers) or less predictable (place names). The change in identification performance within each session indexed perceptual learning. Neuroanatomical associations of degraded speech processing were assessed using voxel-based morphometry. RESULTS: Patients with non-fluent and logopenic progressive aphasia and typical Alzheimer's disease showed impaired identification of sine-wave numbers, whereas all syndromic groups showed impaired identification of sine-wave place names. A significant overall identification advantage for numbers over place names was shown by patients with typical Alzheimer's disease, patients with semantic progressive aphasia and healthy control participants. All syndromic groups showed spontaneous perceptual learning effects for sine-wave numbers. For the combined patient cohort, grey matter correlates were identified across a distributed left hemisphere network extending beyond classical speech-processing cortices. CONCLUSIONS: These findings demonstrate resilience of auditory perceptual learning capacity across dementia syndromes, despite variably impaired perceptual decoding of degraded speech and reduced predictive integration of semantic knowledge. This work has implications for the neurobiology of dynamic sensory processing and plasticity in neurodegenerative diseases and for development of novel biomarkers and therapeutic interventions.