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Learning or identifying dynamics from a sequence of high-dimensional observations is a difficult challenge in many domains, including reinforcement learning and control. The problem has recently been studied from a generative perspective through latent dynamics: high-dimensional observations are embedded into a lower-dimensional space in which the dynamics can be learned. Despite some successes, latent dynamics models have not yet been applied to real-world robotic systems where learned representations must be robust to a variety of perceptual confounds and noise sources not seen during training. In this paper, we present a method to jointly learn a latent state representation and the associated dynamics that is amenable for long-term planning and closed-loop control under perceptually difficult conditions. As our main contribution, we describe how our representation is able to capture a notion of heteroscedastic or input-specific uncertainty at test time by detecting novel or out-of-distribution (OOD) inputs. We present results from prediction and control experiments on two image-based tasks: a simulated pendulum balancing task and a real-world robotic manipulator reaching task. We demonstrate that our model produces significantly more accurate predictions and exhibits improved control performance, compared to a model that assumes homoscedastic uncertainty only, in the presence of varying degrees of input degradation.