Forward process: pick two images: $I^c$ is the image we condition on, $I^t$ is the image whose probability we predict. Extract patches $Q^c$ and $Q^t$ from each , and compute $P(Q^t | Q^c)$

\begin{aligned} v(x) &= N_\theta^{AB}(x) - N_\theta^{BA}(x) \\ \frac{\partial}{\partial t} \Phi^{AB}(x, t) &= v(x)\\ \Phi^{AB}(x, 0) &= x \\ \Phi^{AB}(x) &= \Phi^{AB}(x, 1) \end{aligned}

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