Inverse design is a common yet challenging engineering problem, particularly for nonlinear functional responses such as mechanical behavior or spectral analysis. Deep generative models are motivated by intractability, non-existence or non-uniqueness of solutions, and the need for rapid solution-space exploration. In this study, we show that deep generative model-based and optimization-based approaches can provide incomplete solutions or hallucinate given out-of-distribution targets. To address this, we propose the Generative and Uncertainty-informed Inverse Design (GUIDe) framework, which leverages probabilistic machine learning, statistical inference, and Markov chain Monte Carlo to generate designs with targeted nonlinear behaviors. Instead of inverse mappings, i.e., response $\mapsto$ design, GUIDe adopts design $\mapsto$ response: a forward model predicts each design's nonlinear functional response and evaluates the confidence under a user-specified tolerance. Sampling the solution space by this confidence yields diverse feasible designs. Our validation on nacre-inspired materials finds solutions beyond the training range, even under out-of-distribution targets.

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