Extracting class activation maps (CAM) is a key step for weakly-supervised semantic segmentation (WSSS). The CAM of convolution neural networks fails to capture long-range feature dependency on the image and result in the coverage on only foreground object parts, i.e., a lot of false negatives. An intuitive solution is ``coupling'' the CAM with the long-range attention matrix of visual transformers (ViT) We find that the direct ``coupling'', e.g., pixel-wise multiplication of attention and activation, achieves a more global coverage (on the foreground), but unfortunately goes with a great increase of false positives, i.e., background pixels are mistakenly included. This paper aims to tackle this issue. It proposes a new method to couple CAM and Attention matrix in a probabilistic Diffusion way, and dub it AD-CAM. Intuitively, it integrates ViT attention and CAM activation in a conservative and convincing way. Conservative is achieved by refining the attention between a pair of pixels based on their respective attentions to common neighbors, where the intuition is two pixels having very different neighborhoods are rarely dependent, i.e., their attention should be reduced. Convincing is achieved by diffusing a pixel's activation to its neighbors (on the CAM) in proportion to the corresponding attentions (on the AM). In experiments, our results on two challenging WSSS benchmarks PASCAL VOC and MS~COCO show that AD-CAM as pseudo labels can yield stronger WSSS models than the state-of-the-art variants of CAM.