Before revision: This paper introduces a general framework for explicitly constructing universal deep neural models with inputs from a complete, separable, and locally-compact metric space \mathcal{X outputs in the Wasserstein-1  P_1( \mathcal{Y .
After revision: This paper introduces a general framework for approximating regular conditional distributions (RCDs). Our approximations of these RCDs are implemented by a new class of geometric deep learning models with inputs from a complete, separable, and locally-compact metric space \mathcal{X outputs in the Wasserstein-1 P_1( \mathcal{Y .