To improve accuracy and efficiency of object detection and classification with hyperspectral imagery (HSI), we propose a novel smoothing algorithm by coupling of a Laplacian-based reaction term to a classical divergence-based anisotropic diffusion partial differential equation (PDE). In addition, an adaptive parameter is introduced to regularize this nonlinear reaction-diffusion PDE by explicitly integrating the interband correlations with the noise level of each band in HSI. It is also well-known that the interband correlations can be implicitly embedded into the diffusion coefficient of the divergence-based PDE, to allow a selective smoothing that reduces the local homogeneous area variability while preventing smoothing across edges. Therefore, the interband correlations in HSI are exploited in the proposed method in both explicit and implicit ways. As a result, our algorithm is more effective at controlling the behavior of the diffusion evolution when compared to previous multi/hyperspectral diffusion algorithms. The simulations based on both synthetic data and real hyperspectral remote sensing data show that our algorithm can improve the hyperspectral data quality in terms of both visual inspection and image quality indices.