Diffusion models have shown superior performance on unsupervised anomaly detection tasks. Since trained with normal data only, diffusion models tend to reconstruct normal counterparts of test images with certain noises added. However, these methods treat all potential anomalies equally, which may cause two main problems. From the global perspective, the difficulty of reconstructing images with different anomalies is uneven. Therefore, instead of utilizing the same setting for all samples, we propose to predict a particular denoising step for each sample by evaluating the difference between image contents and the priors extracted from diffusion models. From the local perspective, reconstructing abnormal regions differs from normal areas even in the same image. Theoretically, the diffusion model predicts a noise for each step, typically following a standard Gaussian distribution. However, due to the difference between the anomaly and its potential normal counterpart, the predicted noise in abnormal regions will inevitably deviate from the standard Gaussian distribution. To this end, we propose introducing synthetic abnormal samples in training to encourage the diffusion models to break through the limitation of standard Gaussian distribution, and a spatial-adaptive feature fusion scheme is utilized during inference. With the above modifications, we propose a global and local adaptive diffusion model (abbreviated to GLAD) for unsupervised anomaly detection, which introduces appealing flexibility and achieves anomaly-free reconstruction while retaining as much normal information as possible. Extensive experiments are conducted on three commonly used anomaly detection datasets (MVTec-AD, MPDD, and VisA) and a printed circuit board dataset (PCB-Bank) we integrated, showing the effectiveness of the proposed method.