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Traditional model-based deep learning methods rely heavily on the accuracy of forward models, which can be limiting due to model simplifications or uncertainties. To address this, an untrained forward model residual block that enhances data consistency in the measurement domain for each instance has been proposed. This approach is less parameter-sensitive, requires no additional data, and allows for simultaneous fitting of the forward model and reconstruction in a single pass, benefiting both linear and nonlinear inverse problems. This approach of integrating untrained neural networks within model-based architectures has demonstrated significant improvements in removing artifacts and preserving details across various applications, showcasing its robustness and effectiveness in handling model mismatches.