Diffusion models have demonstrated powerful data generation capabilities in various research fields such as image generation. However, in the field of vibration signal generation, the criteria for evaluating the quality of the generated signal are different from that of image generation and there is a fundamental difference between them. At present, there is no research on the ability of diffusion model to generate vibration signal. In this paper, a Time Series Diffusion Method (TSDM) is proposed for vibration signal generation, leveraging the foundational principles of diffusion models. The TSDM uses an improved U-net architecture with attention block, ResBlock and TimeEmbedding to effectively segment and extract features from one-dimensional time series data. It operates based on forward diffusion and reverse denoising processes for time-series generation. Experimental validation is conducted using single-frequency, multi-frequency datasets, and bearing fault datasets. The results show that TSDM can accurately generate the single-frequency and multi-frequency features in the time series and retain the basic frequency features for the diffusion generation results of the bearing fault series. It is also found that the original DDPM could not generate high quality vibration signals, but the improved U-net in TSDM, which applied the combination of attention block and ResBlock, could effectively improve the quality of vibration signal generation. Finally, TSDM is applied to the small sample fault diagnosis of three public bearing fault datasets, and the results show that the accuracy of small sample fault diagnosis of the three datasets is improved by 32.380%, 18.355% and 9.298% at most, respectively.