Drifting Fields are not Conservative

ArXi:2604.06333v1 Announce Type: new Drifting models generate high-quality samples in a single forward pass by transporting generated samples toward the data distribution using a vector valued drift field. We investigate whether this procedure is equivalent to optimizing a scalar loss and find that, in general, it is not: drift fields are not conservative - they cannot be written as the gradient of any scalar potential. We identify the position-dependent normalization as the source of non-conservatism.