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To address the drawbacks of continuous partial differential equations, a diffusion method based on spectral graph theory and random walk with restart kernel is proposed, which uses non-subsampled contourlet transform to capture the geometric feature of image. Specifically, a new graph weighting function is constructed based on the geometric feature. Moreover, a second-order random walk with restart kernel was generated. The derivation shows that the proposed method is equivalent to the denoising methods based on partial differential equations. The simulation results demonstrate that the proposed method can effectively reduce Gaussian noise and preserve image edge with superior performance compared with other graph-based partial differential equation methods.