Speckle patterns generated in a disordered medium carry a lot of information despite the complete randomness in the intensity pattern. When the medium possesses $chi^{(2)}$ nonlinearity, the speckle is sensitive to the phase of the incident fundamental light, as well as the light generated within. Here, we examine the speckle decorrelation in the fundamental and second-harmonic transmitted light as a function of varying power in the fundamental beam. At low powers, the speckle exhibits strong spatial correlations, which decrease with increasing incident power. We measure the statistical distributions of the correlation coefficients, which transform from sharp-peaked distributions at low power, to wide flat distributions at higher power. The average correlation in the second-harmonic speckle decays faster than in the fundamental speckle. Next, we construct a theoretical model, backed up by numerical computations, to obtain deeper physical insights on the faster decorrelations in the second-harmonic light. Whilst providing excellent qualitative agreement with the experiments, the model sheds important light on the contribution of two effects in the correlations, namely, the generation of second-harmonic light, and the propagation thereof.
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