Memory management apparatus comprises input circuitry to receive a translation request defining a first memory address within a first memory address space; prediction circuitry to generate a predicted second memory address within a second memory address space as a predicted translation of the first memory address, the predicted second memory address being a predetermined function of the first memory address; control circuitry to initiate processing of the predicted second memory address; translation and permission circuitry to perform an operation to generate a translated second memory address for the first memory address associated with permission information to indicate whether memory access is permitted to the translated second memory address; and output circuitry to provide the translated second memory address as a response to the translation request when the permission information indicates that access is permitted to the translated second memory address.