Many deployments require a model to move rapidly from a data-rich source to a related target observed only sparsely. This is especially consequential where target data are difficult to collect, as in healthcare settings with persistent population or acquisition imbalances. Retraining or fine-tuning a high-capacity generator for every target is costly and can be statistically unreliable when target data are scarce. We introduce Meta-Diff, which instead learns a recurring source--target relation once in a compact task space. A shared encoder maps each distribution to a low-dimensional coordinate; a learned relation transports a new source coordinate to its predicted target, and a shared diffusion backbone generates from that prediction without target-specific retraining. Controlled Gaussian-mixture experiments identify when this works: task identity must survive the representation, the relation must generalise across tasks, and the source--target shift must leave useful headroom for transport. On held-out CIFAR-100 validation tasks, correct source $+$ transport achieves 13.9% lower mean SW than transport from the wrong source. With validation-selected adaptation settings in the final-test one-target comparison, its mean SW is 14.7% lower than target-only modelling and 32.7% lower than full fine-tuning; the main route itself uses no target image and assumes the applicable relation is known. On matched CIFAR test episodes, generating from the clean-source coordinate and then applying the known corruption yields lower SW than task-space transport. Office-Home exposes a complementary boundary: transport can align target-domain statistics without reliable object identity. Together, these results recast extreme-few-shot adaptation as reusable transport in task space, while making the conditions for its success and failure directly measurable.

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