Training deep learning models on brain MRI is often plagued by small sample size, which can lead to biased training or overfitting. One potential solution is to synthetically generate realistic MRIs via generative models such as Generative Adversarial Network (GAN). However, existing GANs for synthesizing realistic brain MRIs largely rely on image-to-image conditioned transformations requiring extensive, well-curated pairs of MRI samples for training. On the other hand, unconditioned GAN models (i.e., those generating MRI from random noise) are unstable during training and tend to produce blurred images during inference. Here, we propose an efficient strategy that generates high fidelity 3D brain MRI via Diffusion Probabilistic Model (DPM). To this end, we train a conditional DPM with attention to generate an MRI sub-volume (a set of slices at arbitrary locations) conditioned on another subset of slices from the same MRI. By computing attention weights from slice indices and using a mask to encode the target and conditional slices, the model is able to learn the long-range dependency across distant slices with limited computational resources. After training, the model can progressively synthesize a new 3D brain MRI by generating the first subset of slices from random noise and conditionally generating subsequent slices. Based on 1262 t1-weighted MRIs from three neuroimaging studies, our experiments demonstrate that the proposed method can generate high quality 3D MRIs that share the same distribution as real MRIs and are more realistic than the ones produced by GAN-based models.