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We present a primal only derivation of Mirror Descent as a "partial"discretization of gradient flow on a Riemannian manifold where the metrictensor is the Hessian of the Mirror Descent potential. We contrast thisdiscretization to Natural Gradient Descent, which is obtained by a "full"forward Euler discretization. This view helps shed light on the relationshipbetween the methods and allows generalizing Mirror Descent to generalRiemannian geometries, even when the metric tensor is {\em not} a Hessian, andthus there is no "dual."

Mirrorless Mirror Descent: A Natural Derivation of Mirror Descent