Computer simulations are indispensable for analyzing complex systems, yet high-fidelity models often incur prohibitive computational costs. Multi-fidelity frameworks address this challenge by combining inexpensive low-fidelity simulations with costly high-fidelity simulations to improve both accuracy and efficiency. However, certain scientific problems demand even more accurate results than the highest-fidelity simulations available, particularly when a tuning parameter controlling simulation accuracy is available, but the exact solution corresponding to a zero-valued parameter remains out of reach. In this paper, we introduce the Diffusion Non-Additive (DNA) model, inspired by generative diffusion models, which captures nonlinear dependencies across fidelity levels using Gaussian process priors and extrapolates to the exact solution. The DNA model: (i) accommodates complex, non-additive relationships across fidelity levels; (ii) employs a nonseparable covariance kernel to model interactions between the tuning parameter and input variables, improving predictive performance; (iii) provides closed-form expressions for the posterior predictive mean and variance, allowing efficient inference and uncertainty quantification; and (iv) establishes rigorous theoretical bounds on the prediction error, leading to an optimal experimental design strategy. The methodology is validated on a suite of numerical studies and real-world case studies. An R package implementing the proposed methodology is available to support practical applications.

翻译：计算机模拟对于分析复杂系统不可或缺，然而高保真度模型常因高昂计算成本而难以应用。多保真度框架通过结合低成本的低保真度模拟与昂贵的高保真度模拟，可兼顾精度与效率。然而，当存在控制模拟精度的调优参数且对应零参数的精确解无法获得时，某些科学问题需要比现有最高保真度模拟更精确的结果。受生成式扩散模型启发，本文提出扩散非加性（DNA）模型：该模型利用高斯过程先验捕获保真度层级间的非线性依赖性，并外推至精确解。DNA模型具备以下特性：（i）支持保真度层级间复杂的非加性关系；（ii）采用不可分离协方差核建模调优参数与输入变量的交互作用，提升预测性能；（iii）提供后验预测均值与方差的闭式表达式，实现高效推断与不确定性量化；（iv）建立预测误差的严格理论界，进而推导最优实验设计策略。通过数值算例与真实案例验证了方法的有效性。为支持实际应用，本文提供了实现该方法的R语言软件包。