Though diffusion models excel in image generation, their step-by-step denoising leads to slow generation speeds. Consistency training addresses this issue with single-step sampling but often produces lower-quality generations and requires high training costs. In this paper, we show that optimizing consistency training loss minimizes the Wasserstein distance between target and generated distributions. As timestep increases, the upper bound accumulates previous consistency training losses. Therefore, larger batch sizes are needed to reduce both current and accumulated losses. We propose Adversarial Consistency Training (ACT) , which directly minimizes the Jensen-Shannon (JS)  divergence between distributions at each timestep using a discriminator. Theoretically, ACT enhances generation quality, and convergence. By incorporating a discriminator into the consistency training framework, our method achieves improved FID scores on CIFAR10, ImageNet 6464 and LSUN Cat 256256 datasets, retains zero-shot image inpainting capabilities, and uses less thanof the original batch size and fewer thanof the model parameters and training steps compared to the baseline method, this leads to a substantial reduction in resource consumption.