Stochastic video generation is particularly challenging when the camera is mounted on a moving platform, as camera motion interacts with observed image pixels, creating complex spatio-temporal dynamics and making the problem partially observable. Existing methods typically address this by focusing on raw pixel-level image reconstruction without explicitly modelling camera motion dynamics. We propose a solution by considering camera motion or action as part of the observed image state, modelling both image and action within a multi-modal learning framework. We introduce three models: Video Generation with Learning Action Prior (VG-LeAP) treats the image-action pair as an augmented state generated from a single latent stochastic process and uses variational inference to learn the image-action latent prior; Causal-LeAP, which establishes a causal relationship between action and the observed image frame at time t, learning an action prior conditioned on the observed image states; and RAFI, which integrates the augmented image-action state concept into flow matching with diffusion generative processes, demonstrating that this action-conditioned image generation concept can be extended to other diffusion-based models. We emphasize the importance of multi-modal training in partially observable video generation problems through detailed empirical studies on our new video action dataset, RoAM.