Diffusion-based speech generators are ubiquitous. These methods can generate very high quality synthetic speech and several recent incidents report their malicious use. To counter such misuse, synthetic speech detectors have been developed. Many of these detectors are trained on datasets which do not include diffusion-based synthesizers. In this paper, we demonstrate that existing detectors trained on one such dataset, ASVspoof2019, do not perform well in detecting synthetic speech from recent diffusion-based synthesizers. We propose the Diffusion-Based Synthetic Speech Dataset (DiffSSD), a dataset consisting of about 200 hours of labeled speech, including synthetic speech generated by 8 diffusion-based open-source and 2 commercial generators. We also examine the performance of existing synthetic speech detectors on DiffSSD in both closed-set and open-set scenarios. The results highlight the importance of this dataset in detecting synthetic speech generated from recent open-source and commercial speech generators.