Smartphone-based contactless fingerphoto authentication has become a reliable alternative to traditional contact-based fingerprint biometric systems owing to rapid advances in smartphone camera technology. Despite its convenience, fingerprint authentication through fingerphotos is more vulnerable to presentation attacks, which has motivated recent research efforts towards developing fingerphoto Presentation Attack Detection (PAD) techniques. However, prior PAD approaches utilized supervised learning methods that require labeled training data for both bona fide and attack samples. This can suffer from two key issues, namely (i) generalization:the detection of novel presentation attack instruments (PAIs) unseen in the training data, and (ii) scalability:the collection of a large dataset of attack samples using different PAIs. To address these challenges, we propose a novel unsupervised approach based on a state-of-the-art deep-learning-based diffusion model, the Denoising Diffusion Probabilistic Model (DDPM), which is trained solely on bona fide samples. The proposed approach detects Presentation Attacks (PA) by calculating the reconstruction similarity between the input and output pairs of the DDPM. We present extensive experiments across three PAI datasets to test the accuracy and generalization capability of our approach. The results show that the proposed DDPM-based PAD method achieves significantly better detection error rates on several PAI classes compared to other baseline unsupervised approaches.