  We introduce FedDM, a novel training framework designed for the federated
training of diffusion models. Our theoretical analysis establishes the
convergence of diffusion models when trained in a federated setting, presenting
the specific conditions under which this convergence is guaranteed. We propose
a suite of training algorithms that leverage the U-Net architecture as the
backbone for our diffusion models. These include a basic Federated Averaging
variant, FedDM-vanilla, FedDM-prox to handle data heterogeneity among clients,
and FedDM-quant, which incorporates a quantization module to reduce the model
update size, thereby enhancing communication efficiency across the federated
network.
  We evaluate our algorithms on FashionMNIST (28x28 resolution), CIFAR-10
(32x32 resolution), and CelebA (64x64 resolution) for DDPMs, as well as LSUN
Church Outdoors (256x256 resolution) for LDMs, focusing exclusively on the
imaging modality. Our evaluation results demonstrate that FedDM algorithms
maintain high generation quality across image resolutions. At the same time,
the use of quantized updates and proximal terms in the local training objective
significantly enhances communication efficiency (up to 4x) and model
convergence, particularly in non-IID data settings, at the cost of increased
FID scores (up to 1.75x).
