Idempotent filters in Mule ensure only unique messages are processed by checking message IDs. They can use different object stores like in-memory, file-based, or managed stores to check for duplicate message IDs. This document demonstrates configuring idempotent filters with simple-text-file-store, in-memory-store, and managed-store object stores. The examples show how idempotent filters can prevent duplicate messages from being processed in a Mule flow.