How to train Diffusion model with additional loss?

I would like to train a diffusion model with an additional loss on the created image. Without getting into too much details my intention is to do something like regularization, for example you may think that I want to make sure the created image is smooth, or something of the sort. My thinking was to add an additional loss during training, if the vanilla training process is: $$L = ||\epsilon-\epsilon_\theta(x_t, t)||$$ where $\epsilon_\theta$ is the model learning to predict the noise $\epsilon$ added to the original image. My suggested loss is: $$L = ||\epsilon-\epsilon_\theta(x_t, t)|| + \lambda * L'(img_\theta)$$ where $L'$ is my additional loss (which may for example induce smoothness or whatever), $img_\theta$ is the image that we get after denoising $x_t$ using the predicted noise. For standart models it is trivial that this makes sense. Due to the iterative nature of diffusion models I'm not sure if specifically for them it makes sense. I wasn't able to find any work that does something like this, would appreciate any help, does my additional loss makes sense to add?