We present a novel denoising-diffusion-based generative model framework for predicting synthetic nonlinear fluid fields. The model utilizes forward and inverse diffusion processes to learn complex representations of high-dimensional dynamic systems and predict spatial-temporal evolution trajectories by sampling from learned posteriors. Additionally, we introduce a modified physics-informed loss that provides a physically meaningful regularization in the training pipelines. We demonstrate the model's predictive capacity in different experiments using numerical simulations. We examine the predictive capacity of the model both qualitatively and quantitatively. Results show that the model predicts fluid features associated with spatial-temporal coordinates without numerically solving fluid-governing partial differential equations. Overall, this work demonstrates the potential of denoising diffusion generative models as a promising direction for further investigation into developing new computational fluid dynamics tools and broader applications.