We review the potential to develop sources for neutron scattering science and propose that a merger with the rapidly developing field of inertial fusion energy could provide a major step-change in performance. In stark contrast to developments in synchrotron and laser science, the past 40 years have seen only a factor of 10 increase in neutron source brightness. With the advent of thermonuclear ignition in the laboratory, coupled to innovative approaches in how this may be achieved, we calculate that a neutron source three orders of magnitude more powerful than any existing facility can be envisaged on a 20- to 30-year time scale. Such a leap in source power would transform neutron scattering science.