The problem of persistence in simple diffusion with stochastic initial conditions is discussed. The calculated persistence exponent, which is at variance with that obtained by Majumdar et al [Phys Rev Lett 77, 2867, (1996)] and Derrida et al [Phys Rev Lett 77, 2871,(1996)] numerically, is discussed along with a critical analysis of accepted results. The approach is further extended to the case of advection of a passive scalar by a stochastic velocity field to show that the persistence exponent changes continuously as the velocity field is switched on.