nn.DataParallel adds a .module attribute to the model, so that you might see these key errors while trying to load a state_dict from a plain PyTorch model.
You could either add/remove the .module keys manually or store and load the state_dict using the plain model without the nn.DataParallel wrapper.
To store the state_dict you would use torch.save(model.module.state_dict(), path), while you could just load the state_dict before wrapping the model into nn.DataParallel.