Eq. 14 in the original "Variational Diffusion Models" paper version 1

[cxw-droid]

Hi, thank you for your paper demystifying the "Variational Diffusion Models". In the original paper Variational Diffusion Models version 1 and 2, there is an equation (Eq. 14) that describe a reverse SDE, where $$f(t) = \frac{d\textbf{log}\alpha_t}{dt}$$ and $g^2(t)=\frac{d\sigma^2(t)}{dt} - 2\frac{d\textbf{log}\alpha_t}{dt} \sigma^2(t)$ Would you like to show how the author get this equation? I cannot find it in your current paper. This equation was referenced in other papers such as Progressive Distillation for Fast Sampling of Diffusion Models, see p13

[fabio-deep]

Hi, thanks :)

As we focused on the variational perspective rather than SDEs we chose not to include that derivation. What you're looking for can be found in Appendix E here, and Appendix B of the original paper here.

Best, Fabio

[cxw-droid]

Thank you for introducing this paper. Although I did not find the derivation of the SDE there, the paper looks interesting.

[fabio-deep]

No worries! To clarify, that paper translates the notation from the original SDE paper into VDM's, the actual derivation is in the former as mentioned.

Best, Fabio