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Text-guided image-to-image diffusion models excel in translating images based on textual prompts, allowing for precise and creative visual modifications. However, such a powerful technique can be misused for *spreading misinformation*, *infringing on copyrights*, and *evading content tracing*. This motivates us to introduce the task of origin **ID**entification for text-guided **I**mage-to-image **D**iffusion models (**ID$\mathbf{^2}$**), aiming to retrieve the original image of a given translated query. A straightforward solution to ID$^2$ involves training a specialized deep embedding model to extract and compare features from both query and reference images. However, due to *visual discrepancy* across generations produced by different diffusion models, this similarity-based approach fails when training on images from one model and testing on those from another, limiting its effectiveness in real-world applications. To solve this challenge of the proposed ID$^2$ task, we contribute the first dataset and a theoretically guaranteed method, both emphasizing generalizability. The curated dataset, **OriPID**, contains abundant **Ori**gins and guided **P**rompts, which can be used to train and test potential **ID**entification models across various diffusion models. In the method section, we first prove the *existence* of a linear transformation that minimizes the distance between the pre-trained Variational Autoencoder embeddings of generated samples and their origins. Subsequently, it is demonstrated that such a simple linear transformation can be *generalized* across different diffusion models. Experimental results show that the proposed method achieves satisfying generalization performance, significantly surpassing similarity-based methods (+31.6% mAP), even those with generalization designs. The project is available at https://id2icml.github.io.