Cache-aided coded content delivery is studied for devices with diverse quality-of-service (QoS) requirements, specified by a different average distortion target. The network consists of a server holding a database of independent contents, and users equipped with local caches of different capacities. User caches are filled by the server during a low traffic period without the knowledge of particular user demands. As opposed to the current literature, which assumes that the users request files in their entirety, it is assumed that the users in the system have distinct distortion requirements; and therefore, each user requests a single file from the database to be served at a different distortion level. Our goal in this work is to characterize the minimum delivery rate the server needs to transmit over an error-free shared link to satisfy all possible demand combinations at the requested distortion levels, considering both centralized and decentralized cache placement.