Counterfactual explanations (CEs) aim to enhance the interpretability of machine learning models by illustrating how alterations in input features would affect the resulting predictions. Common CE approaches require an additional model and are typically constrained to binary counterfactuals. In contrast, we propose a novel method that operates directly on the latent space of a generative model, specifically a Diffusion Autoencoder (DAE). This approach offers inherent interpretability by enabling the generation of CEs and the continuous visualization of the model's internal representation across decision boundaries. Our method leverages the DAE's ability to encode images into a semantically rich latent space in an unsupervised manner, eliminating the need for labeled data or separate feature extraction models. We show that these latent representations are helpful for medical condition classification and the ordinal regression of severity pathologies, such as vertebral compression fractures (VCF) and diabetic retinopathy (DR). Beyond binary CEs, our method supports the visualization of ordinal CEs using a linear model, providing deeper insights into the model's decision-making process and enhancing interpretability. Experiments across various medical imaging datasets demonstrate the method's advantages in interpretability and versatility. The linear manifold of the DAE's latent space allows for meaningful interpolation and manipulation, making it a powerful tool for exploring medical image properties. Our code is available at https://doi.org/10.5281/zenodo.13859266.
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