#probability-flow-ode

Question 1: Select all that apply

For a forward SDE $d\mathbf{x} = \mathbf{f}(\mathbf{x}, t)\,dt + g(t)\,d\mathbf{w}$ , a diffusion model can sample either with the reverse SDE $d\mathbf{x} = [\mathbf{f} - g^2\,\nabla_\mathbf{x}\log p_t]\,dt + g\,d\mathbf{w}$ or with the probability-flow ODE $d\mathbf{x} = [\mathbf{f} - \tfrac12 g^2\,\nabla_\mathbf{x}\log p_t]\,dt$ . Which statements are true? Select all that apply.

Both, started from $p_T$ and run from $t = T$ back to 0, pass through the same marginals $p_t$ as the forward process1
The ODE has no noise term, so a given starting point is always mapped to the same sample2
Apart from $\mathbf{f}$ and $g$ , both need only the score $\nabla_\mathbf{x}\log p_t$ , which a network learns by denoising3
The ODE uses half the score weight because it takes twice as many steps as the SDE4
Only the reverse SDE can generate samples; the ODE can only evaluate likelihoods5

#probability-flow-ode

Timed test