  We present a new mode of hydrogen burning on neutron stars (NSs) called
diffusive nuclear burning (DNB). In DNB, the burning occurs in the
exponentially suppressed tail of hydrogen that extends to the hotter regions of
the envelope where protons are readily captured. Diffusive nuclear burning
changes the compositional structure of the envelope on timescales $\sim
10^{2-4} {\rm yrs}$, much shorter than otherwise expected. This mechanism is
applicable to the physics of young pulsars, millisecond radio pulsars (MSPs)
and quiescent low mass X-ray binaries (LMXBs).
