Biometric authentication service providers often claim that it is not possible to reverse-engineer a user's raw biometric sample, such as a fingerprint or a face image, from its mathematical (feature-space) representation. In this paper, we investigate this claim on the specific example of deep neural network (DNN) embeddings. Inversion of DNN embeddings has been investigated for explaining deep image representations or synthesizing normalized images. Existing studies leverage full access to all layers of the original model, as well as all possible information on the original dataset. For the biometric authentication use case, we need to investigate this under adversarial settings where an attacker has access to a feature-space representation but no direct access to the exact original dataset nor the original learned model. Instead, we assume varying degree of attacker's background knowledge about the distribution of the dataset as well as the original learned model (architecture and training process). In these cases, we show that the attacker can exploit off-the-shelf DNN models and public datasets, to mimic the behaviour of the original learned model to varying degrees of success, based only on the obtained representation and attacker's prior knowledge. We propose a two-pronged attack that first infers the original DNN by exploiting the model footprint on the embedding, and then reconstructs the raw data by using the inferred model. We show the practicality of the attack on popular DNNs trained for two prominent biometric modalities, face and fingerprint recognition. The attack can effectively infer the original recognition model (mean accuracy 83\% for faces, 86\% for fingerprints), and can craft effective biometric reconstructions that are successfully authenticated with 1-vs-1 authentication accuracy of up to 92\% for some models.