Numerical simulation of flow and transport in heterogeneous formations has long been studied, especially for uncertainty quantification and risk assessment. The high computational cost associated with running largeâscale numerical simulations in a Monte Carlo sense has motivated the development of surrogate models, which aim to capture the important inputâoutput relations of physicsâbased models but require only a fraction of the cost of full model runs. In this work, we formulate a conditional deep convolutional generative adversarial network (cDCâGAN) surrogate model to learn the dynamic functional mappings in multiphase models. The cDCâGAN belongs to a class of semisupervised learning methods that can be used to learn the data generation processes. Like the original GAN, a main strength of the cDCâGAN is that it includes a selfâtraining scheme for improving the quality of generative modeling in a game theoretic framework, without requiring extensive statistical knowledge and assumptions on input data distributions. In particular, our cDCâGAN model is designed to learn crossâdomain mappings between highâdimensional input (e.g., permeability) and output (e.g., phase saturations) pairs, with the ability to incorporate conditioning information (e.g., prediction time). As a use case, we demonstrate the performance of cDCâGAN for predicting the migration of carbon dioxide (CO2) plume in heterogeneous carbon storage reservoirs, which has both numerical and practical significance because of the safe storage requirements now mandated in many countries. Results show that cDCâGAN achieves high accuracy in predicting the spatial and temporal evolution patterns of the injected CO2 plume, as compared to the original results obtained using a compositional reservoir simulator. The performance of cDCâGAN models, trained using the same number of training samples, stays relatively robust when the level of spatial heterogeneity is increased. Our cDCâGAN is pattern based and is not limited by the underlying physics. Thus, it provides a general framework for developing surrogate models, and for conducting uncertainty analyses for a wide range of physicsâbased models used in both groundwater and subsurface energy exploration applications.