Abstract: The consequences of spatial coordinate transformation in multi-field inflation are studied. Among the spontaneously broken de Sitter isometries, only dilatation in the comoving gauge preserves the form of the metric and thus results in quantum-protected Slavnov-Taylor identities. The corresponding consistency relations between correlation functions of cosmological perturbations are derived in two different ways, by the connected and one-particle-irreducible Green's functions. The lowest-order consistency relations are explicitly given, and even in multi-field inflation the consistency relations in the soft limit are independent of the detail of the matter sector.