  This paper introduces the Variational Determinant Estimator (VDE), a
variational extension of the recently proposed determinant estimator discovered
by arXiv:2005.06553v2. Our estimator significantly reduces the variance even
for low sample sizes by combining (importance-weighted) variational inference
and a family of normalizing flows which allow density estimation on
hyperspheres. In the ideal case of a tight variational bound, the VDE becomes a
zero variance estimator, and a single sample is sufficient for an exact (log)
determinant estimate.
