If gamma‐ray bursts (GRBs), or a subset thereof, are caused by thermonuclear flashes on the surface of a strongly magnetized neutron star, accretion during quiescent intervals between the bursts will give rise to a diffuse background emission from a possibly very large number of sources, each of which is too faint to be detected. A comparison of the expected intensity in this background with observed diffuse background signals in the appropriate energy band may in principle provide a test of the thermonuclear‐flash model, which is independent of (i) the distance scale to GRB sources, (ii) the possible anisotropy of the emission in both the GRB and the accretion energy, (iii) the accretion rates of individual sources and (coupled to this) (iv) the recurrence time of GRBs.