Recent 3D generative models, which are capable of generating full object shapes from just a few images, now open up new opportunities in robotics. In this work, we show that 3D generative models can be used to augment a dataset from a single real-world demonstration, after which an omnidirectional policy can be learned within this imagined dataset. We found that this enables a robot to perform a task when initialised from states very far from those observed during the demonstration, including starting from the opposite side of the object relative to the real-world demonstration, significantly reducing the number of demonstrations required for policy learning. Through several real-world experiments across tasks such as grasping objects, opening a drawer, and placing trash into a bin, we study these omnidirectional policies by investigating the effect of various design choices on policy behaviour, and we show superior performance to recent baselines which use alternative methods for data augmentation.