equation of cfg

[Fusroda-h]

I was digging into the DiT paper and noticed something weird with the classifier-free guidance (CFG) equation. It seems like there might be a mistake compared to the original CFG formulation.

In the DiT paper, the equation is written as:

ε̂_θ(x_t, c) = ε_θ(x_t, ∅) + s * 🔴∇_x log p(x|c)
             ∝ ε_θ(x_t, ∅) + s * (ε_θ(x_t, c) - ε_θ(x_t, ∅))

But shouldn't it be:

ε̂_θ(x_t, c) = ε_θ(x_t, ∅) + s * 🔵∇_x log p(c|x)
             ∝ ε_θ(x_t, ∅) + s * (ε_θ(x_t, c) - ε_θ(x_t, ∅))

From what I understand, the guidance term should involve
∇_x log p(c|x), not ∇_x log p(x|c).
Can someone confirm if this is indeed an error, or am I missing something here?
Appreciate any insights!

FYR.
✔ DiT

✔ CFG