Visual motion distorts the perceived position of a stimulus. In the flash-drag effect (FDE), the perceived position of a flash appears to be shifted in the direction of nearby motion. In the flash-lag effect (FLE), a flash adjacent to a moving stimulus appears to lag behind. The FLE has been explained by several models, including the differential latency hypothesis, that a moving stimulus has a shorter processing latency than a flash does. The FDE even occurs when the flash is presented earlier than the moving stimulus, and it has been discussed whether this temporal property can be explained by the differential latency model. In the present study, we simultaneously quantified the FDE and FLE using the random jump technique (Murakami, 2001b) and compared their temporal properties. While the positional offset between a randomly jumping stimulus and a flashed stimulus determined the FLE, a drifting grating appeared next to the flash at various stimulus-onset asynchronies to induce the FDE. The grating presented up to 200 ms after the flash onset induced the FDE, whose temporal tuning was explained by a simple convolution model incorporating stochastic fluctuations of differential latency estimated from the FLE data and a transient-sustained temporal profile of motion signals. Thus, a common temporal mechanism to compute the stimulus position in reference to surrounding stimuli governs both the FDE and the FLE.