Reconstruction of complete seismic data is a crucial step in seismic data processing, which has seen the application of various convolutional neural networks (CNNs). These CNNs typically establish a direct mapping function between input and output data. In contrast, diffusion models which learn the feature distribution of the data, have shown promise in enhancing the accuracy and generalization capabilities of predictions by capturing the distribution of output data. However, diffusion models lack constraints based on input data. In order to use the diffusion model for seismic data interpolation, our study introduces conditional constraints to control the interpolation results of diffusion models based on input data. Furthermore, we improving the sampling process of the diffusion model to ensure higher consistency between the interpolation results and the existing data. Experimental results conducted on synthetic and field datasets demonstrate that our method outperforms existing methods in terms of achieving more accurate interpolation results.