  Diffusion models are known to be vulnerable to outliers in training data. In
this paper we study an alternative diffusion loss function, which can preserve
the high quality of generated data like the original squared $L_{2}$ loss while
at the same time being robust to outliers. We propose to use pseudo-Huber loss
function with a time-dependent parameter to allow for the trade-off between
robustness on the most vulnerable early reverse-diffusion steps and fine
details restoration on the final steps. We show that pseudo-Huber loss with the
time-dependent parameter exhibits better performance on corrupted datasets in
both image and audio domains. In addition, the loss function we propose can
potentially help diffusion models to resist dataset corruption while not
requiring data filtering or purification compared to conventional training
algorithms.
