Automatic speaker verification (ASV) systems are highly vulnerable to presentation attacks, also called spoofing attacks. Replay is among the simplest attacks to mount - yet difficult to detect reliably. The generalization failure of spoofing countermeasures (CMs) has driven the community to study various alternative deep learning CMs. The majority of them are supervised approaches that learn a human-spoof discriminator. In this paper, we advocate a different, deep generative approach that leverages from powerful unsupervised manifold learning in classification. The potential benefits include the possibility to sample new data, and to obtain insights to the latent features of genuine and spoofed speech. To this end, we propose to use variational autoencoders (VAEs) as an alternative backend for replay attack detection, via three alternative models that differ in their class-conditioning. The first one, similar to the use of Gaussian mixture models (GMMs) in spoof detection, is to train independently two VAEs - one for each class. The second one is to train a single conditional model (C-VAE) by injecting a one-hot class label vector to the encoder and decoder networks. Our final proposal integrates an auxiliary classifier to guide the learning of the latent space. Our experimental results using constant-Q cepstral coefficient (CQCC) features on the ASVspoof 2017 and 2019 physical access subtask datasets indicate that the C-VAE offers substantial improvement in comparison to training two separate VAEs for each class. On the 2019 dataset, the C-VAE outperforms the VAE and the baseline GMM by an absolute 9 - 10% in both equal error rate (EER) and tandem detection cost function (t-DCF) metrics. Finally, we propose VAE residuals - the absolute difference of the original input and the reconstruction as features for spoofing detection.