Lithology identification is one of the key steps in the exploration and development of oil and gas resources. At present, using deep learning technology to identify lithology in logging can significantly improve the identification speed and accuracy. However, due to the shortage of data in logging data sets and the uneven distribution of lithology categories, the neural network is prone to overfitting in the training process, resulting in a decrease in the accuracy of the model. In order to solve these problems, a lithology identification model LogDiffusion based on diffusion probability model is proposed in this paper, which can generate high quality logging data and be used for training, so as to improve the classification accuracy of lithology identification. Based on the traditional diffusion probability model and considering the one-dimensional structure of log data, a fractional network FT-Unet for gradient estimation is designed in this paper, and an auxiliary classifier FT-Transformer is proposed to obtain accurate lithology labels. In addition, a threshold based dynamic labeling mechanism is proposed to improve the accuracy of the sampling algorithm. The experimental results on two small-sample blind well logging data sets show that this method can alleviate the problems of insufficient data quantity and uneven distribution of lithology categories in the logging data set to a certain extent, so as to improve the accuracy and precision of lithology identification.