Artificial intelligence (AI) has shown promising results for computational pathology tasks. However, one of the limitations in clinical practice is that these algorithms are optimised for the distribution represented by the training data. For out-of-distribution (OOD) data, they often deliver predictions with equal confidence, even though these often are incorrect. In the pursuit of OOD detection in digital pathology, this study evaluates the state-of-the-art (SOTA) in computational pathology OOD detection, based on diffusion probabilistic models, specifically by adapting the latent diffusion model (LDM) for this purpose (AnoLDM). We compare this against post-hoc methods based on the latent space of foundation models, which are SOTA in general computer vision research. The approaches are not only evaluated on data from the same medical centres as the training set, but also on several datasets with data distribution shifts. The results show that AnoLDM performs similarly well or better than diffusion model based approaches published in previous studies in computational pathology but with reduced computational costs. However, our optimal configuration of an approach based on foundation models (kang_residual) outperforms AnoLDM on OOD detection on data not experiencing any covariate shifts, with an AUROC of 96.17 versus 91.86. Interestingly, AnoLDM is more successful at handling the data distribution shifts investigated in this study. However, both AnoLDM and kang_residual suffer substantial loss in the performance under the data distribution shifts, hence future work should focus on improving the generalisation of OOD detection for computational pathology applications.