We introduce funion, a system providing end-to-end sender-receiver unlinkability for neural network inference. By leveraging the Pigeonhole storage protocol and BACAP (blinding-and-capability) scheme from the Echomix anonymity system, funion inherits the provable security guarantees of modern mixnets. Users can anonymously store input tensors in pseudorandom storage locations, commission compute services to process them via the neural network, and retrieve results with no traceable connection between input and output parties. This store-compute-store paradigm masks both network traffic patterns and computational workload characteristics, while quantizing execution timing into public latency buckets. Our security analysis demonstrates that funion inherits the strong metadata privacy guarantees of Echomix under largely the same trust assumptions, while introducing acceptable overhead for production-scale workloads. Our work paves the way towards an accessible platform where users can submit fully anonymized inference queries to cloud services.