  We present a new method of training energy-based models (EBMs) for anomaly
detection that leverages low-dimensional structures within data. The proposed
algorithm, Manifold Projection-Diffusion Recovery (MPDR), first perturbs a data
point along a low-dimensional manifold that approximates the training dataset.
Then, EBM is trained to maximize the probability of recovering the original
data. The training involves the generation of negative samples via MCMC, as in
conventional EBM training, but from a different distribution concentrated near
the manifold. The resulting near-manifold negative samples are highly
informative, reflecting relevant modes of variation in data. An energy function
of MPDR effectively learns accurate boundaries of the training data
distribution and excels at detecting out-of-distribution samples. Experimental
results show that MPDR exhibits strong performance across various anomaly
detection tasks involving diverse data types, such as images, vectors, and
acoustic signals.
