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Time series prediction is a widespread and well studied problem with applications in many domains (medical, geoscience, network analysis, finance, econometry etc.). In the case of multivariate time series, the key to good performances is to properly capture the dependencies between the variates. Often, these variates are structured, i.e. they are localised in an abstract space, usually representing an aspect of the physical world, and prediction amounts to a form of diffusion of the information across that space over time. Several neural network models of diffusion have been proposed in the literature. However, most of the existing proposals rely on some a priori knowledge on the structure of the space, usually in the form of a graph weighing the pairwise diffusion capacity of its points. We argue that this piece of information can often be dispensed with, since data already contains the diffusion capacity information, and in a more reliable form than that obtained from the usually largely hand-crafted graphs. We propose instead a fully data-driven model which does not rely on such a graph, nor any other prior structural information. We conduct a first set of experiments to measure the impact on performance of a structural prior, as used in baseline models, and show that, except at very low data levels, it remains negligible, and beyond a threshold, it may even become detrimental. We then investigate, through a second set of experiments, the capacity of our model in two respects: treatment of missing data and domain adaptation.