Hi, in Karrasâ€˜s paper Elucidating the Design Space of Diffusion-Based Generative Models, they specify sigma_{data} as 0.5, where is number come from?

Thatâ€™s the standard deviation of the data. If you look at a more recent paper [2312.02696] Analyzing and Improving the Training Dynamics of Diffusion Models, that paper actually uses different data, so they could have used a different sigma_data; but instead they normalize the data to have standard deviation 0.5 so that they donâ€™t have to change the other hyperparameters of EDM.