  We develop an effective theory of pulse propagation in a nonlinear {\it and}
disordered medium. The theory is formulated in terms of a nonlinear diffusion
equation. Despite its apparent simplicity this equation describes novel
phenomena which we refer to as "locked explosion" and "diffusive" collapse. The
equation can be applied to such distinct physical systems as laser beams
propagating in disordered photonic crystals or Bose-Einstein condensates
expanding in a disordered environment.
