When humans use vision to gauge the travel distance of an extended forward movement, they often underestimate the movement's extent. This underestimation can be explained by leaky path integration, an integration of the movement to obtain distance. Distance underestimation occurs because this integration is imperfect and contains a leak that increases with distance traveled. We asked human observers to estimate the distance from a starting location for visually simulated movements in a virtual environment. The movements occurred along curved paths that veered left and right around a central forward direction. In this case, the distance that has to be integrated (i.e., the beeline distance between origin and endpoint) and the distance that is traversed (the path length along the curve) are distinct. We then tested whether the leak accumulated with distance from the origin or with traversed distance along the curved path. Leaky integration along the path makes the seemingly counterintuitive prediction that the estimated origin-to-endpoint distance should decrease with increasing veering, because the length of the path over which the integration occurs increases, leading to a larger leak effect. The results matched the prediction: movements of identical origin-to-endpoint distance were judged as shorter when the path became longer. We conclude that leaky path integration from visual motion is performed along the traversed path even when a straight beeline distance is calculated.