Unsupervised anomaly detection, which learns only from normal images, is a central task in medical image analysis and remains an open problem. Reconstruction-based methods pass an image through an encoder-decoder network trained on normal data and detect anomalies from the residual between the image and its reconstruction. This works only if the information passed from the encoder to the decoder is limited; otherwise the network learns an identity mapping and reconstructs anomalies too. This limit is usually imposed through architectural choices, tuned per dataset, that cannot be stated in bits. We introduce the quasi-binarizing (QB) layer, which squashes each latent element into [0, 1] and adds Laplace noise of scale 1/epsilon. Each element is then epsilon-locally differentially private, and the mutual information between an image and its reconstruction is bounded by a quantity that depends only on epsilon and the number of QB elements, whatever the encoder and decoder. Placing a QB layer on every encoder-decoder path, including all skip connections, we build QBAE, a seven-level attention U-Net with 32,768 QB elements. On the seven datasets of the MedIAnomaly benchmark, QBAE with one architecture and one configuration reaches a mean image-level AUROC of 0.828, the highest among methods that do not adapt to each dataset, and the best reported results on BraTS2021 (AUROC 0.911, pixel-level AP 0.838). The noise is kept at test time, so that every reconstruction satisfies the bound. Without input corruption, the bottleneck alone prevents identity collapse (mean AUROC 0.805 vs. 0.590). Code is available at https://github.com/hanaokalog/MedIAnomalyQB.

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