Joint-Domain Implicit Conditional Density Estimation under Sparse Structured Coverage

Conditional density estimation (CDE) aims to estimate the full conditional distribution \(p(y\mid x)\). We study CDE under sparse coverage of ordered or gridded conditioning domains. Structure-aware CDE approaches typically encode cross-condition sharing through prespecified analytic relational functions, such as kernels or covariance functions. While effective when well matched to the data, the chosen functional family can restrict the form of admissible interactions. We introduce Joint-domain Implicit Conditional Density Estimation (JICDE), which represents \({p(y\mid x):x\in\mathcal T}\) as the location-wise marginals of a stochastic generator defined jointly over the conditioning domain. JICDE retains the geometry and locality of the conditioning domain as architectural inductive biases, while parameterizing the detailed cross-condition sharing rule through shared learnable local transformations, allowing the induced sharing behavior to adapt across different structural regimes. Across ordered and gridded structured CDE benchmarks, JICDE consistently compares favorably with representative CDE and structured probabilistic baselines.