Studying the spatiotemporal evolution of scientific phenomena often relies on costly simulations and experiments. Machine learning-based surrogate models reduce this cost, but most are limited to deterministic forward prediction. Scientific temporal analysis often requires both forward prediction and backward inference, while temporal evolution is not always uniquely determined, especially for the inverse problem. We introduce DiffUNet^2, a bidirectional conditional diffusion model for probabilistic scientific temporal prediction. It supports both forward and backward prediction within a shared model. We evaluate DiffUNet^2 on four scientific temporal datasets spanning fluid dynamics, chemical reaction dynamics, and material deformation, against deterministic and probabilistic baselines. Results show that DiffUNet^2 achieves strong predictive performance in both temporal directions and high probabilistic ensemble quality compared with existing baselines. To support practical scientific exploration beyond prediction, we further extend DiffUNet^2's generation ability with target-guided state editing, allowing states of interest to be specified and explored in both temporal directions.

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