We consider the interaction of vortices of different size and strength (vorticity) and a diffusion flame of N-2-diluted H-2 and air stabilized on an opposed-jet burner. In our direct numerical simulations, which take into account the effects of detailed chemistry and transport, we demonstrate the effects of flame curvature of opposite orientations by placing a vortex on either the air or the fuel side of the diffusion flame. When the flame curvature is convex towards the fuel stream, the flame burns more intensely even at a scalar dissipation rate, chi, close to the critical (extinction) value, chi (c), of the flat one-dimensional diffusion flame (for the same composition of the reactant streams). On the other hand, if the flame curvature is convex towards the air stream, the flame weakens and in some cases extinguishes even when the local chi is significantly lower than chi (c). Depending on the curvature orientation, the extinction scalar dissipation rate can vary considerably. This observation raises questions on the common use of a single extinction scalar dissipation rate in many turbulent diffusion flame simulations. Our results indicate that the role of curvature in the transient flame-vortex interaction is similar to what was observed in previous studies of steady curved flames. We also observe that the reignition process following local extinction is two-dimensional. The reignition process observed in our simulations may not be described well by flamelet models (steady or transient) that are based on one-dimensional formulations.