Conditional generative models, particularly diffusion-based methods, have recently been applied to graph prediction by modeling the target as a conditional distribution given the input graph, yielding competitive results compared to deterministic predictor. However, existing diffusion-based prediction methods typically require expensive iterative denoising at inference and often suffer from unstable sampling, which motivates recent efforts to reduce inference denoising steps and enable stable sampling via techniques such as consistency training. Despite this progress, we find that existing consistency training methods for graph prediction could potentially fall into a shortcut solution: the model may attempt to satisfy the self-consistency constraint by ignoring the noisy target (i.e., assigning it negligible weight), ultimately collapsing into a purely deterministic predictor. To mitigate such shortcut solution, we propose GCCM, a graph contrastive consistency model that goes beyond isolated pairwise matching between the same target at different noise levels by introducing negative pairs into a contrastive consistency objective. This adds an additional separation requirement, making the shortcut solution no longer trivially sufficient to satisfy the proposed objective. Moreover, we apply feature perturbation to the input node/edge features to break identical conditioning on the input graph, so that the shortcut no longer yields the same predictions across noise levels and becomes less attractive. Extensive experiments on benchmark datasets demonstrate that GCCM mitigates the shortcut solution and yields consistent performance improvements in graph prediction compared to deterministic predictors.