  Many compression techniques have been proposed to reduce the communication
overhead of Federated Learning training procedures. However, these are
typically designed for compressing model updates, which are expected to decay
throughout training. As a result, such methods are inapplicable to downlink
(i.e., from the parameter server to clients) compression in the cross-device
setting, where heterogeneous clients $\textit{may appear only once}$ during
training and thus must download the model parameters. Accordingly, we propose
$\textsf{DoCoFL}$ -- a new framework for downlink compression in the
cross-device setting. Importantly, $\textsf{DoCoFL}$ can be seamlessly combined
with many uplink compression schemes, rendering it suitable for bi-directional
compression. Through extensive evaluation, we show that $\textsf{DoCoFL}$
offers significant bi-directional bandwidth reduction while achieving
competitive accuracy to that of a baseline without any compression.
