  A generalized uncertainty principle is obtained from a conformally
transformed action containing a scalar field and a unique constraint. The
constraint's Lagrange multiplier is found to obey a relativistic diffusion
equation transforming the internal coordinates of the scalar field, via the
shift theorem. For an approximately conserved Noether current, the coupled
wave- and diffusion-like equations are merged into an infinite-order partial
differential equation (PDE). It is conjectured that infrared and ultraviolet
divergences are naturally removed in studying the infinite-order PDE's
corresponding propagator. It is further suggested that higher-order
contributions of the associated commutation relations are reminiscent of a
self-interaction not present in the current quantum theory.
