Multi-period distributionally robust optimization (DRO) is in general not time consistent. For a given multi-period DRO problem with generalized moments ambiguity, we propose an Ambiguity Updating Robust Architecture (AURA) that constructs the ambiguity set of all conditional distributions-to-go, given the realized uncertainty. We prove that AURA is time consistent, but is more conservative than the original DRO and is equal if and only if DRO was originally time consistent. AURA’s robust counterpart is a deterministic dynamic program. When the support of the uncertainty is continuous, AURA contains all deterministic distributions, thus is as conservative as parameter robustness. We term this “ambiguity collapse”. We trace the origins of ambiguity collapse to distributions that become deterministic after some particular history is traversed. We term these “conditionally clairvoyant” distributions. We propose a regularization of the original DRO ambiguity set to remove such distributions; doing so allows ambiguity collapse to be avoided. These results are illustrated using a stylized numerical experiment on a water management setting.