Objective and background This study aimed to develop a deep convolutional neural network (DCNN) model capable of generating synthetic 4D magnetic resonance angiography (MRA) from 3D time-of-flight (TOF) images, allowing estimation of temporal changes in arterial flow. TOF MRA provides static information about arterial structures through maximum intensity projection (MIP) processing, but it does not capture the dynamic information of contrast agent circulation, which is lost during MIP processing. Considering the principles of TOF, it is hypothesized that dynamic information about arterial blood flow is latent within TOF signals. Although arterial spin labeling (ASL) can extract dynamic arterial information, ASL MRA has drawbacks, such as longer imaging times and lower spatial resolution than TOF MRA. This study's primary aim is to extend the utility of TOF MRA by training a machine-learning model on paired TOF and ASL data to extract latent dynamic information from TOF signals. Methods A DCNN combining a modified U-Net and a long-short-term memory (LSTM) network was trained on a dataset of 13 subjects (11 menand two women, aged 42-77 years) using paired 3D TOF MRA and 4D ASL MRA images. Subjects had no history of cerebral vessel occlusion or significant stenosis. The dataset was acquired using a 3T MRI system with a 32-channel head coil. Preprocessing involved resampling and intensity normalization of TOF and ASL images, followed by data augmentation and arterial mask generation. The model learned to extract flow information from TOF images and generate 8-phase 4D MRA images. The precision of flow estimation was evaluated using the coefficient of determination (R²) and Bland-Altman analysis. A board-certified neuroradiologist validated the quality of the images and the absence of significant stenosis in the major cerebral arteries. Results The generated 4D MRA images closely resembled the ground-truth ASL MRA data, with R² values of 0.92, 0.85, and 0.84 for the internal carotid artery (ICA), proximal middle cerebral artery (MCA), and distal MCA, respectively. Bland-Altman analysis revealed a systematic error of -0.06, with 95% agreement limits ranging from -0.18 to 0.12. Additionally, the model successfully identified flow abnormalities in a subject with left MCA stenosis, displaying a delayed peak and subsequent flattening distal to the stenosis, indicative of reduced blood flow. Visualization of the predicted arterial flow overlaid on the original TOF MRA images highlighted the spatial progression and dynamics of the flow. Conclusions The DCNN model effectively generated synthetic 4D MRA images from TOF images, demonstrating its potential to estimate temporal changes in arterial flow accurately. This non-invasive technique offers a promising alternative to conventional methods for visualizing and evaluating healthy and pathological flow dynamics. It has significant potential to improve the diagnosis and treatment of cerebrovascular diseases by providing detailed temporal flow information without the need for contrast agents or invasive procedures. The practical implementation of this model could enable the extraction of dynamic cerebral blood flow information from routine brain MRI examinations, contributing to the early diagnosis and management of cerebrovascular disorders.