  The dually flat structure of statistical manifolds can be derived in a
non-parametric way from a particular case of affine space defined on a
qualified set of probability measures. The statistically natural displacement
mapping of the affine space depends on the notion of Fisher's score. The model
space must be carefully defined if the state space is not finite. Among various
options, we discuss how to use Orlicz-Sobolev spaces with Gaussian weight. Such
a fully non-parametric set-up provides tools to discuss intrinsically
infinite-dimensional evolution problems.
