UniGradICON is a foundation model for medical image registration that addresses the limitations of current methods. Traditional registration methods are accurate but slow, while deep learning-based methods are fast and accurate but not generic. UniGradICON combines the speed and accuracy of deep learning with the generality of traditional methods, offering a universal registration model that can handle various anatomical regions, modalities, and acquisitions without retraining. It achieves this by using a weaker regularizer, GradICON, which allows the model to learn transformations supported by the data, enabling training with consistent hyperparameters across different datasets. UniGradICON was trained on twelve public datasets and evaluated extensively, showing strong performance on both in-distribution and out-of-distribution tasks. It can provide zero-shot capabilities for new registration tasks and serves as a strong initialization for fine-tuning on out-of-distribution datasets. The model is available for use and will be periodically updated to include more anatomical regions, modalities, and deformation patterns. UniGradICON demonstrates strong performance on various registration tasks, outperforming conventional methods and task-specific deep learning models in some cases. It is a strong out-of-the-box baseline for medical image registration, offering a balance between speed, accuracy, and generality. The model is supported by NIH grants and has been tested on various datasets, including those from the Osteoarthritis Initiative, Human Connectome Project, and COPDGene study. The results show that UniGradICON can generalize well to unseen anatomical regions, modalities, and tasks, and can be further improved with additional training data and self-supervised learning techniques.UniGradICON is a foundation model for medical image registration that addresses the limitations of current methods. Traditional registration methods are accurate but slow, while deep learning-based methods are fast and accurate but not generic. UniGradICON combines the speed and accuracy of deep learning with the generality of traditional methods, offering a universal registration model that can handle various anatomical regions, modalities, and acquisitions without retraining. It achieves this by using a weaker regularizer, GradICON, which allows the model to learn transformations supported by the data, enabling training with consistent hyperparameters across different datasets. UniGradICON was trained on twelve public datasets and evaluated extensively, showing strong performance on both in-distribution and out-of-distribution tasks. It can provide zero-shot capabilities for new registration tasks and serves as a strong initialization for fine-tuning on out-of-distribution datasets. The model is available for use and will be periodically updated to include more anatomical regions, modalities, and deformation patterns. UniGradICON demonstrates strong performance on various registration tasks, outperforming conventional methods and task-specific deep learning models in some cases. It is a strong out-of-the-box baseline for medical image registration, offering a balance between speed, accuracy, and generality. The model is supported by NIH grants and has been tested on various datasets, including those from the Osteoarthritis Initiative, Human Connectome Project, and COPDGene study. The results show that UniGradICON can generalize well to unseen anatomical regions, modalities, and tasks, and can be further improved with additional training data and self-supervised learning techniques.