Process fault is one of the main reasons that a system may appear unreliable, and it affects the safety of a system. The existence of different degrees of noise in the industry also makes it difficult to extract the effective features of the data for the fault diagnosis method based on deep learning. In order to solve the above problems, this paper improves the deep belief network (DBN) and iterates the optimal penalty term by introducing a penalty factor, avoiding the local optimal situation of a DBN and improving the accuracy of fault diagnosis in order to minimize the impact of noise while improving fault diagnosis and process safety. Using the adaptive noise reduction capability of an adaptive lifting wavelet (ALW), a practical chemical process fault diagnosis model (ALW-DBN) is finally proposed. Then, according to the Tennessee–Eastman (TE) benchmark test process, the ALW-DBN model is compared with other methods, showing that the fault diagnosis performance of the enhanced DBN combined with adaptive wavelet denoising has been significantly improved. In addition, the ALW-DBN shows better performance under the influence of different noise levels in the acid gas absorption process, which proves its high adaptability to different noise levels.