Appendixfor RiemannianContinuousNormalizingFlows

In the following, we provide a brief overview of Riemannian geometry and constant curvature manifolds, specifically the Poincaré ball and the hypersphere models. Sphere In the two-dimensional settingd = 2, we rely on polar coordinates to parametrize the sphere S2. In the following subsection we remind that this regularization term can also be motivated from an estimator'svarianceperspective. 5 D.2 Frobeniusnorm Hutchinson'sestimator Hutchinson'sestimator(Hutchinson,1990)isasimple waytoobtain a stochastic estimate ofthetrace ofamatrix. The variance of this estimator thus depends on the Frobenius norm of the vector's field Jacobian Thenγ(tn) is also a Cauchy sequence by Equation 16. So for every sequence (tn) in (a,b) that converges tob, we have that(γ(tn)) converges top.