Score identity Distillation (SiD) is a data-free method that has achieved state-of-the-art performance in image generation by leveraging only a pretrained diffusion model, without requiring any training data. However, the ultimate performance of SiD is constrained by the accuracy with which the pretrained model captures the true data scores at different stages of the diffusion process. In this paper, we introduce SiDA (SiD with Adversarial Loss), which not only enhances generation quality but also improves distillation efficiency by incorporating real images and adversarial loss. SiDA utilizes the encoder from the generator's score network as a discriminator, boosting its ability to distinguish between real images and those generated by SiD. The adversarial loss is batch-normalized within each GPU and then combined with the original SiD loss. This integration effectively incorporates the average "fakeness" per GPU batch into the pixel-based SiD loss, enabling SiDA to distill a single-step generator either from scratch or by fine-tuning an existing one. SiDA converges significantly faster than its predecessor when trained from scratch, and swiftly improves upon the original model's performance after an initial warmup period during fine-tuning from a pre-distilled SiD generator. This one-step adversarial distillation method has set new benchmarks for generation performance when distilling EDM diffusion models pretrained on CIFAR-10 (32x32) and ImageNet (64x64), achieving FID scores of $\mathbf{1.499}$ on CIFAR-10 unconditional, $\mathbf{1.396}$ on CIFAR-10 conditional, and $\mathbf{1.110}$ on ImageNet 64x64. Our open-source code will be integrated into the SiD codebase on GitHub.