BACKGROUND: The mouse model is the most widely used animal model in neuroscience, yet translating findings to humans suffers from the lack of formal models comparing the mouse and the human brain. Here, we devised a framework using mouse and human gene expression to build a quantitative common space and apply it to models of neurodegenerative disease. METHODS: We trained a variational autoencoder on mouse spatial transcriptomics, and embedded mouse and human gene orthologs in the model's latent space. We computed a latent cross-species similarity matrix for translation and compared translated maps to human ground truth evidence. FINDINGS: We established the validity of our model based on anatomical homology. Independent of species, brain areas with similar latent patterns clustered together, improving the homology of known anatomical pairs, and preserving principles of brain organisation. Importantly, translating brain alterations in mouse disease models predicted human patterns of brain changes in Alzheimer's and Parkinson's diseases. We further determined the best mouse model for the AD patients, based on how well the translations matched the patient data, across multiple models and timepoints. INTERPRETATION: Our work provides i) a quantitative bridge across evolutionary divergence between the human and the predominant preclinical species, ii) a predictive framework to help design and evaluate disease models. By highlighting which models are best suited across stages of disease, we effectively support the understanding of disease mechanisms, assist in the workflow of clinical trials, and ultimately accelerate the transformation of findings into improved human outcomes. FUNDING: Supported by the Biotechnology and Biological Sciences Research Council (BBSRC) UK, the Medical Research Council (MRC) UK, the European Research Council, and the NIHR Oxford Health Biomedical Research Centre.