1. An ultrasound diagnostic apparatus comprising: an ultrasound transceiving unit configured to transmit ultrasound waves toward a subject to be examined into which a puncture tool is inserted, receive reflected waves of an ultrasound waves reflected from the subject and the puncture tool, and generate echo signals of time-sequential frames based on the received reflected waves; an ultrasound image generation unit configured to generate an ultrasound image of the subject based on the echo signals generated by the ultrasound transceiving unit; an image display unit configured to display the ultrasound image generated by the ultrasound image generation unit; a differential echo signal generation unit configured to generate a differential echo signal between time-sequential frames from the echo signals of the time-sequential frames that are acquired during inserting the puncture tool in the subject at a predetermined angle; a tip candidate detection unit configured to perform a tip detection process based on the differential echo signal generated by the differential echo signal generation unit to thereby detect at least one tip candidate including a tip end of the puncture tool; and a tip candidate processing unit configured to highlight a tip candidate of the puncture tool detected by the tip candidate detection unit to thereby generate a tip image in which one or more tip candidates of the puncture tool are highlighted, wherein the image display unit displays the tip image of the puncture tool highlighted by the tip candidate processing unit so as to be superimposed on the ultrasound image generated by the ultrasound image generation unit, wherein the differential echo signal generation unit generates a differential image based on the generated differential echo signal, wherein the tip candidate detection unit performs the tip detection process on the differential mage generated by the differential echo signal generation unit to detect the tip candidate of the puncture tool, and wherein the differential echo signal generation unit adjusts a time difference between the time-sequential frames used for generating the differential image in accordance with an insertion speed of the puncture tool.