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We propose a novel optimization-based paradigm for 3D human model fitting on images and scans. In contrast to existing approaches that directly regress the parameters of a low-dimensional statistical body model (e.g. SMPL) from input images, we train an ensemble of per-vertex neural fields network. The network predicts, in a distributed manner, the vertex descent direction towards the ground truth, based on neural features extracted at the current vertex projection. At inference, we employ this network, dubbed LVD, within a gradient-descent optimization pipeline until its convergence, which typically occurs in a fraction of a second even when initializing all vertices into a single point. An exhaustive evaluation demonstrates that our approach is able to capture the underlying body of clothed people with very different body shapes, achieving a significant improvement compared to state-of-the-art. LVD is also applicable to 3D model fitting of humans and hands, for which we show a significant improvement to the SOTA with a much simpler and faster method.