  Neural ordinary differential equations (NODEs) is an invertible neural
network architecture promising for its free-form Jacobian and the availability
of a tractable Jacobian determinant estimator. Recently, the representation
power of NODEs has been partly uncovered: they form an $L^p$-universal
approximator for continuous maps under certain conditions. However, the
$L^p$-universality may fail to guarantee an approximation for the entire input
domain as it may still hold even if the approximator largely differs from the
target function on a small region of the input space. To further uncover the
potential of NODEs, we show their stronger approximation property, namely the
$\sup$-universality for approximating a large class of diffeomorphisms. It is
shown by leveraging a structure theorem of the diffeomorphism group, and the
result complements the existing literature by establishing a fairly large set
of mappings that NODEs can approximate with a stronger guarantee.
