As latent diffusion models (LDMs) democratize image generation capabilities, there is a growing need to detect fake images. A good detector should focus on the generative model’s fingerprints while ignoring image properties such as semantic content, resolution, file format, etc. Fake image detectors are usually built in a data-driven way, where a model is trained to separate real from fake images. Existing works primarily investigate network architecture choices and training recipes. In this work, we argue that in addition to these algorithmic choices, we also require a well-aligned dataset of real/fake images to train a robust detector. For the family of LDMs, we propose a very simple way to achieve this: we reconstruct all the real images using the LDM's autoencoder, without any denoising operation. We then train a model to separate these real images from their reconstructions. The fakes created this way are extremely similar to the real ones in almost every aspect (e.g., size, aspect ratio, semantic content), which forces the model to look for the LDM decoder's artifacts. We empirically show that this way of creating aligned real/fake datasets, which also sidesteps the computationally expensive denoising process, helps in building a detector that focuses less on spurious correlations, something that a very popular existing method is susceptible to. Finally, to demonstrate the effectivenss of dataset alignment, we build a detector using images that are not natural objects, and present promising results. Overall, our work identifies the subtle but significant issues that arise when training a fake image detector and proposes a simple and inexpensive solution to address these problems.