Unsupervised deep image prior (DIP) addresses shortcomings of training data requirements and limited generalization associated with supervised deep learning. The performance of DIP depends on the network architecture and the stopping point of its iterative process. Optimizing these parameters for a new image requires time, restricting DIP application in domains where many images need to be processed. Focusing on fluorescence microscopy data, we hypothesize that similar images share comparable optimal parameter configurations for DIP-based denoising, potentially enabling optimization-free DIP for fluorescence microscopy. We generated a calibration (n=110) and validation set (n=55) of semantically different images from an open-source dataset for a network architecture search targeted towards ideal U-net architectures and stopping points. The calibration set represented our transfer basis. The validation set enabled the assessment of which image similarity criterion yields the best results. We then implemented AUTO-DIP, a pipeline for automatic parameter transfer, and compared it to the originally published DIP configuration (baseline) and a state-of-the-art image-specific variational denoising approach. We show that a parameter transfer from the calibration dataset to a test image based on only image metadata similarity (e.g., microscope type, imaged specimen) leads to similar and better performance than a transfer based on quantitative image similarity measures. AUTO-DIP outperforms the baseline DIP (DIP with original DIP parameters) as well as the variational denoising approaches for several open-source test datasets of varying complexity, particularly for very noisy inputs. Applications to locally acquired fluorescence microscopy images further proved superiority of AUTO-DIP.