Digital twins are often built under the assumption that greater model fidelity leads to better downstream performance. We show that this is not always the case: retaining weakly dependent or auxiliary degrees of freedom can increase the dimensionality of learning and control problems enough that a sparse stochastic surrogate outperforms even an exact high-dimensional model. To identify such structure, we introduce a framework for dependence discovery directly at the level of the full conditional law. The method combines conditional generative modeling with Gaussian-process distillation and kernel mode decomposition to quantify how strongly individual variables enter the conditional distribution, including through variability, tails, multimodality, and other features invisible to the conditional mean. The resulting dependence structure can be used both to construct sparse stochastic digital twins from data and to reduce known high-dimensional models for downstream tasks. In a modified Lunar Lander problem, an eight-dimensional sparse surrogate yields better control performance than the exact 109-dimensional simulator despite lower transition fidelity. A stochastic heat-equation example shows that the framework recovers sparse structure in a 102-dimensional data-driven setting and produces a more effective surrogate than one conditioned on all candidate inputs, while economic data demonstrate its use for identifying time-varying memory structure. These results show that model fidelity and downstream utility are distinct objectives, and that dependence discovery provides a practical route to sparse stochastic digital twins.

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