  Anomalies are by definition rare, thus labeled examples are very limited or
nonexistent, and likely do not cover unforeseen scenarios. Unsupervised
learning methods that don't necessarily encounter anomalies in training would
be immensely useful. Generative vision models can be useful in this regard but
do not sufficiently represent normal and abnormal data distributions. To this
end, we propose constant curvature manifolds for embedding data distributions
in unsupervised visual anomaly detection. Through theoretical and empirical
explorations of manifold shapes, we develop a novel hyperspherical Variational
Auto-Encoder (VAE) via stereographic projections with a gyroplane layer - a
complete equivalent to the Poincar\'e VAE. This approach with manifold
projections is beneficial in terms of model generalization and can yield more
interpretable representations. We present state-of-the-art results on visual
anomaly benchmarks in precision manufacturing and inspection, demonstrating
real-world utility in industrial AI scenarios. We further demonstrate the
approach on the challenging problem of histopathology: our unsupervised
approach effectively detects cancerous brain tissue from noisy whole-slide
images, learning a smooth, latent organization of tissue types that provides an
interpretable decisions tool for medical professionals.
