Rb-82 dynamic cardiac PET imaging is widely used for the clinical diagnosis of coronary artery disease (CAD), but its short half-life results in high noise levels that degrade dynamic frame quality and parametric imaging. The lack of paired clean-noisy training data, rapid tracer kinetics, and frame-dependent noise variations further limit the effectiveness of existing deep learning denoising methods. We propose DECADE (A Temporally-Consistent Unsupervised Diffusion model for Enhanced Rb-82 CArdiac PET DEnoising), an unsupervised diffusion framework that generalizes across early- to late-phase dynamic frames. DECADE incorporates temporal consistency during both training and iterative sampling, using noisy frames as guidance to preserve quantitative accuracy. The method was trained and evaluated on datasets acquired from Siemens Vision 450 and Siemens Biograph Vision Quadra scanners. On the Vision 450 dataset, DECADE consistently produced high-quality dynamic and parametric images with reduced noise while preserving myocardial blood flow (MBF) and myocardial flow reserve (MFR). On the Quadra dataset, using 15%-count images as input and full-count images as reference, DECADE outperformed UNet-based and other diffusion models in image quality and K1/MBF quantification. The proposed framework enables effective unsupervised denoising of Rb-82 dynamic cardiac PET without paired training data, supporting clearer visualization while maintaining quantitative integrity.