1. An X-ray diagnostic apparatus comprising: an X-ray tube configured to generate X-rays; an X-ray detector configured to detect X-rays generated from the X-ray tube and transmitted through a subject; an aperture-variable collimator mechanism configured to limit a radiation field of X-rays from the X-ray tube; an image generation unit configured to repeatedly generate a first X-ray image based on an output from the X-ray detector during a period in which an aperture of the collimator mechanism is a first aperture and to repeatedly generate a second X-ray image based on an output from the X-ray detector during a period in which the aperture is a second aperture smaller than the first aperture; a combining unit configured to repeatedly generate a composite image based on a latest second X-ray image of the repeatedly generated second X-ray images and a specific first X-ray image of the repeatedly generated first X-ray images for the second X-ray image is generated; a display unit configured to display the repeatedly generated composite image as a dynamic image in real time; a determination unit configured to determine whether to update the first X-ray image in the composite image, based on an index associated with an anatomical positional shift between the first X-ray image and the second X-ray image; and a control unit configured to enlarge the aperture of the collimator mechanism from the second aperture to the first aperture by controlling the collimator mechanism when the determination unit determines to update the first X-ray image and to maintain the aperture of the collimator mechanism at the second aperture by controlling the collimator mechanism when the determination unit determines not to update the first X-ray image.