Title: SWIFT: Rapid Decentralized Federated Learning via Wait-Free Model Communication. Abstract: The decentralized Federated Learning (FL) setting avoids the role of a potentially unreliable or untrustworthy central host by utilizing groups of clients to collaboratively train a model via localized training and model/gradient sharing. Most existing decentralized FL algorithms require synchronization of client models where the speed of synchronization depends upon the slowest client. In this work, we propose SWIFT: a novel wait-free decentralized FL algorithm that allows clients to conduct training at their own speed. Theoretically, we prove that SWIFT matches the gold-standard iteration convergence rate $\mathcal{O}(1/\sqrt{T})$ of parallel stochastic gradient descent for convex and non-convex smooth optimization (total iterations $T$). Furthermore, we provide theoretical results for IID and non-IID settings without any bounded-delay assumption for slow clients which is required by other asynchronous decentralized FL algorithms. Although SWIFT achieves the same iteration convergence rate with respect to $T$ as other state-of-the-art (SOTA) parallel stochastic algorithms, it converges faster with respect to runtime due to its wait-free structure. Our experimental results demonstrate that SWIFT's runtime is reduced due to a large reduction in communication time per epoch, which falls by an order of magnitude compared to synchronous counterparts. Furthermore, SWIFT produces loss levels for image classification, over IID and non-IID data settings, upwards of 50\% faster than existing SOTA algorithms.