Bespalov-Talanov theory is extended to the divergent beam in gain medium. The small-scale self-focusing properties are studied systematically in small-signal and saturated gain conditions. In the case of small-signal gain, for a given input power with different initial radiuses, the cutoff spatial frequency, the fastest growing frequency and the maximum growth of small-scale modulation, evolve differently with the change of the small-signal gain and propagation distance. The initial radius represents the degree of diffraction divergence, the decrease of the initial radius can reduce the fastest growing frequency and the maximum perturbation growth. For a given output power, the increase of the small-signal gain can decrease the maximum perturbation growth, while the fastest growing frequency shifts to the lower frequency. Compared with the small-signal gain, the fastest growing frequency and the maximum gain are smaller in medium with saturated gain. In different system design, the amplifier gain and the beam parameters should be weighed and selected properly in practical systems.